KR101489708B1 - Memory control algorithm, method and apparatus using the same for fluid numerical analysis based on lattice boltzmann method - Google Patents

Abstract

According to embodiments of the present invention, a method for a fluid numerical analysis based on the lattice Boltzmann method performed by a computer comprises the steps of: (a) computing particle distribution functions based on the lattice Boltzmann equation in each of a plurality of directions with respect to each of nodes connected to each other in each direction; and (b) advecting the particle distribution functions of the nodes with respect to each direction by replacing a pointer within an address range, where a particle distribution function of a node of interest in a specific direction i is stored, with a pointer indicating a temporary storage space, where the particle distribution function in the specific direction i is copied from a neighboring node opposite to an opposite direction i and is stored, with respect to the specific direction i of the node of interest, in order to spread particle distribution functions of each node to neighboring nodes in an array structure storage space where the particle distribution functions of the nodes are stored in each direction, depending on a result of the computation.

Description

[0001] MEMORY CONTROL ALGORITHM METHOD AND APPARATUS USING THE SAME FOR FLUID NUMERICAL ANALYSIS BASED ON LATTICE BOLTZMANN METHOD [0002]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a fluid numerical analysis technique, and more particularly, to a fluid numerical analysis technique based on a lattice Boltzmann technique.

Fluid simulation is based on the Lagrangian approach based on the interaction between particles and particles, focusing on the behavior of the particles that make up the fluid, and the phenomena that occur at the boundary of the lattice, Based on the Eulerian approach (Eulerian approach) can be roughly divided into.

The Lattice Boltzmann Method (LBM), which uses the Lattice Boltzmann Equation (LBM) among the grid-based techniques, is based on the concept of continuity, Is analyzed in the individual grids while the flow is being analyzed.

Although the Navier-Stokes equation, which is the basic formula for fluid analysis, contains a nonlinear term, it must be assumed appropriately for linearization, very sensitive to boundary conditions, and problematic in convergence of analytical values at irregular boundaries, Since it is linear, the algorithm is relatively simple.

In addition, LBM computes the flow of fluid at each lattice point, so parallelization is possible and is suitable for parallel computing which is spreading recently.

The LBM has two stages of computation: a collision step and a streaming step. The collision calculation step is a step of redistributing the particle distribution functions (pdf) by the collision between the particles in the lattice, and the advection step is a step in which the redistributed directional particle distribution functions, To the grid.

For every lattice point, a particle distribution function is defined for each direction of fluid, and each data is stored in a memory structure called Structure of Array (SoA) with grids and directions in rows and columns, respectively.

Since the data in the array structure must be mutually displaced with respect to each other between neighboring grids during the advection step, an efficient control algorithm for the array structure storage space in which the particle distribution function data is stored becomes necessary.

The conventionally proposed naive memory control algorithm creates an empty new array structure and copies the PDFs to the orientation data locations in the corresponding neighboring grids in the new array structure sequentially for each lattice from the previous array structure, When the copy is completed for the grid, the collision operation step is performed again with the new array structure, and the memory is controlled by emptying the existing array structure for the next advection step.

This nab algorithm doubled memory, which was problematic for large-scale fluid analysis.

In order to solve this problem, the swap memory control algorithm proposed is a method to reduce the memory requirement. First, when the advection phase starts, the position of the particle distribution function data is reversed between directions facing each other in each lattice swap) and an algorithm that controls the memory by swapping the particle distribution function data in the specific direction of the lattice and the particle distribution function data in the facing direction in the neighboring lattice.

The swap algorithm requires as much memory and only a small amount of temporary storage space as an array structure, so the required memory capacity is largely reduced to about half compared with the Naive algorithm. However, instead of simply copying the particle distribution function data, It requires a much larger memory bandwidth, which results in a longer time in the advection step.

In addition, the A-A pattern memory control algorithm is more complicated than the swap memory control algorithm because the memory requirement is about half that of the nave algorithm like the swap memory control algorithm, but is divided into the odd process and the even process. First of all, the AA pattern memory control algorithm is applied in the polyphase flow where the advection step and the collision calculation step are performed in a bundled manner and the density gradient calculation after the advection step and the phase segregation after the collision calculation step have to be performed It is difficult to do.

In this paper, we propose a memory control algorithm that can be applied to multiphase flow without increasing memory capacity.

A problem to be solved by the present invention is to provide a memory control algorithm and a method and an apparatus for numerical analysis of a fluid based on a lattice Boltzmann technique using the same.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a memory control algorithm that does not greatly increase memory capacity in addition to an array structure, and a method and apparatus for fluid numerical analysis based on a Grid Boltzmann technique using the memory control algorithm.

A problem to be solved by the present invention is to provide a memory control algorithm having a low memory bandwidth required to move the particle distribution functions of the respective gratings in the array structure to the neighboring grids in the advection step, To provide.

SUMMARY OF THE INVENTION The present invention is directed to a memory control algorithm that allows a longer simulation to be performed during the same total computation time by reducing the time required for advection, and a method and apparatus for fluid numerical analysis based on a Grid Boltzmann technique using the same. .

The solution to the problem of the present invention is not limited to those mentioned above, and other solutions not mentioned can be clearly understood by those skilled in the art from the following description.

According to an aspect of the present invention, there is provided a computer-implemented lattice Boltzmann technique based fluid numerical analysis method,

(a) computing, for each of the nodes connected to each other in the plurality of directions, the particle distribution functions for each direction based on the lattice Boltzmann equation; And

(b) in order to spread the particle distribution functions of each node to the neighbor nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the operation, By replacing the pointer of the address range in which the particle distribution function of the interested node in the specific direction i is stored as a pointer to the temporary storage space in which the particle distribution function of the specific direction i is copied and stored from the neighboring node facing the direction i ' And aliasing the particle distribution functions of the node of interest with respect to the directions.

According to an embodiment, the step (b)

Creating a temporary storage space for storing particle distribution functions of all nodes with respect to direction i;

Referring to the array structure storage space, a particle distribution function stored in a storage location of a direction i of a neighboring node opposite to i 'in the opposite direction of the node of interest to a storage location of a node of interest in the temporary storage space Storing the particle distribution functions of all nodes with respect to direction i in said temporary storage space with respect to direction i by repeating the storing operation; And

The operation of replacing the pointer of the address range in which the particle distribution functions of all nodes with respect to direction i in the array structure storage space is stored with a pointer of the address range in which the particle distribution functions are stored in the temporary storage space with respect to direction i, And repeating for each.

According to an embodiment, the step (b)

Creating at least two sets of temporary storage spaces for storing respective particle distribution functions of all nodes with respect to at least two directions i and j, respectively;

Referring to the array structure storage space, particle distribution functions stored in storage locations i and j of directions i and j of neighboring nodes, respectively opposite to directions i 'and j' J in the temporary storage spaces with respect to directions i and j, respectively, to the temporary storage spaces with respect to directions i and j, Respectively; And

Pointers of address ranges in which the particle distribution functions of all nodes in relation to directions i and j in the array structure storage space are stored are pointers to address ranges in which particle distribution functions are stored in temporary storage spaces for directions i and j Repeating the replacing operation for each of the direction groups consisting of at least two directions.

According to one embodiment, the step (b)

Generating first and second temporary storage spaces each capable of storing particle distribution functions of a node of interest with respect to a direction i and an opposite direction i ';

Referring to the array structure storage space, a first particle distribution function stored in a storage location of direction i at a first neighbor node opposite to direction i 'of direction i of the interested node is referred to as a first temporary storage space In a storage location of a node of interest in the network;

Referring to the array structure storage space, a second particle distribution function stored in the storage location of the opposite direction i 'at the second neighbor node facing the direction i of the interested node is stored in the second temporary storage space Storing in a storage location of a node of interest;

Replacing the pointer of the address range in which the particle distribution functions of all the nodes are stored in the array structure storage space with respect to the direction i with a pointer of the address range in which the particle distribution functions are stored in the first temporary storage space with respect to the direction i; And

A pointer in the address range in which the particle distribution functions of all nodes are stored in the array structure storage space in the opposite direction i 'is replaced with a pointer in the address range in which the particle distribution functions are stored in the second temporary storage space in the opposite direction i' .

According to one embodiment, the memory space required to provide the temporary storage space in step (b) may be provided utilizing memory space used for temporal storage of the computation results during step (a).

According to one embodiment, in the step (b), the temporary storage space may correspond to an address range that belonged to the array structure storage space with respect to the specific direction and the opposite direction that was immediately preceded.

According to another aspect of the present invention, there is provided a computer-implemented lattice Boltzmann technique-based fluid numerical analysis method,

In order to spread the particle distribution functions of each node to the neighbor nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the collision calculation,

(i) providing a partial array structure storage space including first and second temporary storage spaces for storing the particle distribution functions in direction i of all nodes and the particle distribution functions in opposite direction i ', respectively;

(ii) a first particle distribution function stored in a storage location corresponding to a direction i of a first neighbor node facing the opposite direction i 'of the node of interest, with reference to the array structure storage space, Storing in a storage location of a node of interest in a temporary storage space;

(iii) a second particle distribution function stored in a storage location corresponding to the opposite direction i 'of the second neighbor node facing the direction i of the node of interest, with reference to the array structure storage space, Storing in a storage location of a node of interest in the second temporary storage space;

(iv) repeating steps (ii) through (iii) for all nodes in the array structure storage space;

(v) swapping a pointer of an address range in which particle distribution functions of direction i in the array structure storage space are stored with an address pointer of the first temporary storage space;

(vi) swapping a pointer of the address range in which the particle distribution functions in the opposite direction i 'in the array structure storage space are stored with an address pointer of the second temporary storage space; And

(vii) repeating steps (i) through (vi) for all directions i and the opposite direction i '.

According to one embodiment, the memory space required to provide the first and second temporary storage spaces in the steps (i) to (vii) may include a memory space used for temporal storage of the operation result during the conflict operation step Can be provided.

According to one embodiment, the first and second temporary storage spaces provided in step (i) are arranged in the array structure storage space < RTI ID = 0.0 >Lt; / RTI > may correspond to address ranges that have been in the < / RTI >

According to another aspect of the present invention, there is provided a computer-based lattice Boltzmann technique-based fluid numerical analysis apparatus,

A collision computing unit for computing, based on a grid Boltzmann equation, particle distribution functions for each direction for each of nodes connected to each other in a plurality of directions;

An array structure storage space in which rows and columns are defined by directions and nodes and which also stores particle distribution functions of all nodes by direction, and particle distribution functions of all nodes with respect to at least one specific direction into at least one temporary storage space A memory for providing a partial array structure storage space for storing the partial array structure storage space; And

In order to spread the particle distribution functions of the respective nodes in the array structure storage space according to the result of the operation to the neighboring nodes, a specific direction i from the neighboring node facing the opposite direction i ' The pointer of the address range in which the particle distribution function of the interested node in the specific direction i is stored is replaced with a pointer indicating the temporary storage space in which the particle distribution function of the interested node is copied and stored, And an advection memory control unit for diverting the input signals.

According to one embodiment, the advection memory control unit comprises:

Generating in the memory temporary storage space for storing particle distribution functions of all nodes with respect to direction i,

Referring to the array structure storage space, a particle distribution function stored in a storage location of a direction i of a neighboring node opposite to i 'in the opposite direction of the node of interest to a storage location of a node of interest in the temporary storage space Storing the particle distribution functions of all nodes with respect to direction i in said temporary storage space with respect to direction i,

The operation of replacing the pointer of the address range in which the particle distribution functions of all nodes with respect to direction i in the array structure storage space is stored with a pointer of the address range in which the particle distribution functions are stored in the temporary storage space with respect to direction i, For each < / RTI >

According to one embodiment, the advection memory control unit comprises:

Generating at least two temporary storage spaces in the memory, each of which stores particle distribution functions of all nodes with respect to at least two directions i and j,

Referring to the array structure storage space, particle distribution functions stored in storage locations i and j of directions i and j of neighboring nodes, respectively opposite to directions i 'and j' J in the temporary storage spaces with respect to directions i and j, respectively, to the temporary storage spaces with respect to directions i and j, Respectively,

Pointers of address ranges in which the particle distribution functions of all nodes in relation to directions i and j in the array structure storage space are stored are pointers to address ranges in which particle distribution functions are stored in temporary storage spaces for directions i and j And alternate repeating operations for each of the direction groups consisting of at least two directions.

According to one embodiment, the advection memory control unit comprises:

Generating first and second temporary storage spaces in the memory, each of which can store particle distribution functions of a node of interest with respect to a direction i and an opposite direction i '

Referring to the array structure storage space, a first particle distribution function stored in a storage location of direction i at a first neighbor node opposite to direction i 'of direction i of the interested node is referred to as a first temporary storage space In a storage location of a node of interest within the network,

Referring to the array structure storage space, a second particle distribution function stored in the storage location of the opposite direction i 'at the second neighbor node facing the direction i of the interested node is stored in the second temporary storage space Storing it in a storage location of a node of interest,

A pointer of an address range in which the particle distribution functions of all nodes are stored in the array structure storage space with respect to direction i is replaced with a pointer of an address range in which particle distribution functions are stored in the first temporary storage space with respect to direction i,

A pointer in the address range in which the particle distribution functions of all nodes are stored in the array structure storage space in the opposite direction i 'is replaced with a pointer in the address range in which the particle distribution functions are stored in the second temporary storage space in the opposite direction i' Lt; / RTI >

According to one embodiment, the memory space required to provide the temporary storage space in the memory may be provided utilizing the memory space in which the conflict operation unit is used for temporal storage of operation results.

According to one embodiment, the temporary storage space provided in the memory may correspond to an address range that belonged to the array structure storage space with respect to the specific direction and the opposite direction that was immediately preceded.

According to another aspect of the present invention, there is provided a computer-based grating Boltzmann technique-based fluid numerical analysis apparatus,

A collision computing unit for computing, based on a grid Boltzmann equation, particle distribution functions for each direction for each of nodes connected to each other in a plurality of directions;

An array structure storage space in which rows and columns are defined by directions and nodes and also stores particle distribution functions of all the nodes in a direction and a particle array storage space in which all particle distribution functions of all nodes in a specific direction and a reverse direction are stored in two temporary storage spaces A memory for providing a partial array structure storage space for storing in a memory; And

And an advection memory control unit for diffusing the particle distribution functions of each node into neighboring nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the collision calculation,

Wherein the advection memory control unit comprises:

(i) providing, in the memory, a partial array structure storage space including first and second temporary storage spaces for respectively storing particle distribution functions in direction i of all nodes and particle distribution functions in opposite direction i '

(ii) a first particle distribution function stored in a storage location corresponding to a direction i of a first neighbor node facing the opposite direction i 'of the node of interest, with reference to the array structure storage space, Storing in a storage location of a node of interest in the temporary storage space,

(iii) a second particle distribution function stored in a storage location corresponding to the opposite direction i 'of the second neighbor node facing the direction i of the node of interest, with reference to the array structure storage space, Storing at a storage location of a node of interest in the second temporary storage space,

(iv) repeating steps (ii) to (iii) for all nodes in the array structure storage space,

(v) swapping a pointer of an address range in which the particle distribution functions of direction i in the array structure storage space are stored with an address pointer of the first temporary storage space,

(vi) swapping a pointer of the address range in which the particle distribution functions in the opposite direction i 'in the array structure storage space are stored with the address pointer of the second temporary storage space, and

(vii) repeating steps (i) through (vi) for all directions i and opposite directions i '.

According to one embodiment, the memory space required to provide the first and second temporary storage spaces in steps (i) through (vi) may include a memory space used for temporal storage of the operation result during the conflict operation step Can be provided.

According to one embodiment, the first and second temporary storage spaces provided in step (i) are arranged in the array structure storage space < RTI ID = 0.0 >Lt; / RTI > may correspond to address ranges that have been in the < / RTI >

According to the memory control algorithm of the present invention and the method and apparatus for the fluid numerical analysis based on the lattice Boltzmann technique using the memory control algorithm, it is possible to effectively perform the advection step without significantly increasing the memory capacity in addition to the array structure.

According to the memory control algorithm of the present invention and the method and apparatus for the fluid numerical analysis based on the Grid Boltzmann technique using the memory control algorithm of the present invention, it is possible to lower the memory bandwidth required to move the particle distribution functions of the respective gratings in the array structure to the neighboring grids in the advection step.

According to the memory control algorithm of the present invention and the method and apparatus for the fluid numerical analysis based on the lattice Boltzmann technique using the memory control algorithm, the time required for the advection step can be reduced, and a longer simulation can be performed during the same total computation time.

The effects of the present invention are not limited to those mentioned above, and other effects not mentioned can be clearly understood by those skilled in the art from the following description.

1 is a flow diagram illustrating a method of fluid numerical analysis based on a lattice Boltzmann technique in accordance with an embodiment of the present invention.
FIG. 2 is a flowchart illustrating a method of updating an array structure storage space in a advection step of a fluid-numerical method based on a lattice Boltzmann technique according to an embodiment of the present invention.
3 is a diagrammatic illustration of an array structure storage space and a temporary storage space to be updated with respect to a specific direction in the advection step of the lattice Boltzmann technique based fluid numerical analysis method according to an embodiment of the present invention.
FIG. 4 is a flow chart illustrating a method of copying from a neighboring node of a node of interest to a node of interest in a temporary storage space in an array structure storage space with respect to a specific direction in a advection step of a method of fluid numerical analysis according to an embodiment of the present invention; FIG. 2 is a diagram schematically illustrating a procedure for performing the above process.
FIG. 5 is a flow chart illustrating a procedure for updating a node of interest in an array structure storage space with respect to a specific direction by a node of interest in a temporary storage space, in the advection step of the method of fluid numerical analysis based on the lattice Boltzmann technique according to an embodiment of the present invention Fig.
6 is a block diagram illustrating a lattice Boltzmann technique based fluid numerical analysis apparatus in accordance with another embodiment of the present invention.

For the embodiments of the invention disclosed herein, specific structural and functional descriptions are set forth for the purpose of describing an embodiment of the invention only, and it is to be understood that the embodiments of the invention may be practiced in various forms, The present invention should not be construed as limited to the embodiments described in Figs.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The same reference numerals are used for the same constituent elements in the drawings and redundant explanations for the same constituent elements are omitted.

Throughout the description of the present invention, a node means each of the lattices in which various operations on the Grid Boltzmann technique take place, and thus, substantially the same as the lattice and node Can be used in the same sense.

Throughout the specification of the present invention, the streaming and advection steps may be used interchangeably, unless the context clearly indicates otherwise.

1 is a flow diagram illustrating a method of fluid numerical analysis based on a lattice Boltzmann technique in accordance with an embodiment of the present invention.

The Grid Boltzmann technique-based fluid numerical analysis method is a method for calculating a particle distribution function (pdf) computed with respect to a physical quantity defined for each direction, for example, density, velocity or external force of each fluid, Is a technique of calculating according to the lattice Boltzmann equation as shown in the following equation (1).

는 격자 x 내에서 i번째 방향의 입자 분포 함수이고, e_i는 i번째 방향의 마이크로스코픽 속도(microscopic velocities) 벡터이며, t는 시간, Ω_i는 i 번째 방향의 충돌 연산자(collision operator)이다. 충돌 연산자는 입자의 충돌 시의 거동에 관하여 주어지는 항으로서, 예를 들어 BGK(Bhatnagar-Gross-Krook) 항으로 주어진다.here,

It is a particle distribution function of the i-th direction in the grid x, e _i is the microscopic rate of the i-th direction (microscopic velocities) vector, t is the time, Ω _i is a collision operator (collision operator) of the i-th direction. The collision operator is a term given in terms of the behavior of a particle at the time of impact, for example given as BGK (Bhatnagar-Gross-Krook) term.

Since the time is treated discretely, the lattice Boltzmann operation is performed using the operation result when the time is (t-1), and when the operation at t is completed, the time (T + 1), and the lattice Boltzmann operation is performed when the time is (t + 1) by using the operation result when the time is t, and the previous operation result is used The operation must be repeated continuously.

Accordingly, the lattice Boltzmann equation of Equation (1) can be separated into Equation (2) of the collision calculation step and Equation (3) of the advection step.

는 관심 대상 노드의 충돌 연산 단계의 결과를 일시적으로 저장하는 변수이고,

를 이웃 노드들로 스트리밍한 결과가

이다.here,

Is a variable for temporarily storing the result of the collision calculation step of the node of interest,

Is streamed to neighboring nodes.

to be.

를 관심 대상 노드 x에서 각각 e_i만큼 떨어진 이웃 노드들의 각 방향으로 스트리밍하여

를 얻기 위해

의 어레이 구조와

의 어레이 구조를 별도로 두고

의 어레이 구조를

의 어레이 구조에 그대로 복사함으로써,

의 어레이 구조가 생성된다.In the above-described Naive memory control algorithm

Is streamed in each direction of neighbor nodes separated by e _i from the node of interest x

To get

And

The array structure of the

Array structure of

Lt; RTI ID = 0.0 > array structure,

Lt; / RTI >

의 어레이 구조 내에서 관심 대상 노드 내의 입자 분포 함수 데이터들의 위치를 변경한 다음, 각 방향 별로 관심 대상 노드와 이웃 노드 사이에서 입자 분포 함수 데이터들을 맞바꾸는 식으로 메모리 사용을 최소화하였고, 최종적으로 맞바꾸기가 완료되면

의 어레이 구조가 얻어진다.In addition, the swap memory control algorithm

The memory usage is minimized by changing the location of the particle distribution function data in the target node in the array structure of the target node and then changing the particle distribution function data between the target node and the neighboring node in each direction, Is completed

Is obtained.

On the other hand, in the fluid numerical analysis method based on the lattice Boltzmann technique of the present invention, in step S11 of the collision calculation step, for each of the nodes connected to each other by the plurality of directions, .

Next, in step S12, which is an advection step for spreading the particle distribution functions of the respective nodes to the neighbor nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the collision calculation, With respect to a specific direction i, a pointer to a temporary storage space in which a particle distribution function in a specific direction i is copied and stored from a neighboring node opposed to the opposite direction i ' By replacing the pointer of the stored address range, we node the particle distribution functions of the nodes with respect to each direction.

Herein, the opposite direction i 'indicates the opposite direction forming a straight line with the direction i.

Generating a temporary storage space for storing the particle distribution functions of all the nodes with respect to the direction i; generating a particle distribution function stored in the storage location of the direction i of the neighboring node opposite to i ' i to the temporary storing space related to the direction i by storing the particle distribution functions of all the nodes in the direction i in the storage locations of the interested nodes in the temporary storing space related to the direction i, It is possible to repeat the operation of replacing the pointer of the address range in which the particle distribution functions of the nodes are stored with a pointer of the address range in which the particle distribution functions of the temporary storage space relating to the direction i are stored.

Usually, the streaming step is intuitively understood that the particle distribution functions are propagated from the node of interest to each of the neighboring nodes in each direction. The present invention is characterized in that this process is observed in reverse.

In other words, in the present invention, it is understood that each node propagates the particle distribution functions to each neighbor node one by one in the streaming step, as a result that each node is updated by receiving one of the particle distribution functions from neighboring neighboring nodes .

For example, there are 9 directions (D2Q9 model) for two-dimensional fluid numerical analysis, 15 (D3Q15 model), 19 (D3Q19 model), or 27 (D3Q27 model) . However, these direction numbers include direction 0 corresponding to the origin of the node, and this direction 0 does not move to the neighboring node in the streaming step. Therefore, the number of directions that should actually propagate in the streaming phase is 8 (D2Q9 model) for 2D fluid numerical analysis, 14 (D3Q15 model), 18 (D3Q19 model) or 26 (D3Q27 model).

On the other hand, actually, the particle distribution function data are collectively stored for each direction rather than for each node. In other words, the particle distribution function data for direction i is stored in memory with consecutive addresses within a specific address range in the order of the nodes.

In this array structure, the address range in which the particle distribution data of direction i is continuously stored can be specified by a pointer.

Therefore, the present invention creates an empty temporary storage space for storing the particle distribution function data of direction i, and stores the particle distribution function to be propagated from the neighboring node to the interested node at the time of streaming to the storage location of the interested node of the temporary storage space do.

The creation of the temporary storage space and the storage of the particle distribution function data require as much memory space as the number of particle distribution function data corresponding to direction i, but the present invention can minimize the addition of such memory space.

Specifically, the memory space necessary for providing the temporary storage space of the streaming step can be satisfied by utilizing the memory space for storing the operation result used in the conflict operation step. Since the operation result storage space is necessary for storing the result of performing the operation in each direction in the collision operation step, it is empty without performing any role in the streaming step. Therefore, the operation result storage space is used as a temporary storage space in the streaming step And there is no need for substantially more memory.

At this time, as the advection step is repeatedly performed for each direction, the temporary storage space may be provided corresponding to the address ranges that belonged to the array structure storage space with respect to the specific direction and the opposite direction that were immediately preceded.

Also, since the address range pointer of the temporary storage space relating to the direction i is interchanged with the address range pointer in which the particle distribution function data calculated with respect to the direction i is stored, when a new conflict operation step is started after the streaming step is completed It should be noted that the resultant arithmetic result temporary storage space may have a different address range for each collision calculation step.

Generating at least two temporary storage spaces for storing respective particle distribution functions of all nodes with respect to at least two directions i and j according to an embodiment, And storing the particle distribution functions respectively stored in the storage locations of directions i and j of neighboring nodes respectively opposed to j and j in the storage locations of the interested node in temporary storage spaces related to directions i and j, respectively , Replacing pointers of address ranges in which the particle distribution functions of all nodes with respect to directions i and j are stored with pointers of address ranges in which particle distribution functions are stored in temporary storage spaces with respect to directions i and j, Lt; RTI ID = 0.0 > direction. ≪ / RTI >

In particular, direction j may be in the opposite direction of direction i.

In this case, specifically, first and second temporary storage spaces, each capable of storing the particle distribution functions of the interested node with respect to the direction i and the opposite direction i ', are generated, and the direction i In the storage location of the interested node in the first temporary storage space for direction i, and stores the first particle distribution function stored in the storage location of direction i in the opposite direction The second particle distribution function stored in the storage location of the opposite direction i 'in one second neighbor node may be stored in the storage location of the node of interest in the second temporary storage space with respect to the opposite direction i'.

FIG. 2 is a flowchart illustrating a method of updating an array structure storage space in a advection step of a fluid-numerical method based on a lattice Boltzmann technique according to an embodiment of the present invention.

Referring to FIG. 2, in the advection step, that is, the streaming step for spreading the particle distribution functions of the respective nodes to neighboring nodes in the array structure storage space in which the particle distribution functions of the nodes are stored according to the result of the collision calculation, the particle distribution functions are copied from the array structure storage space to the temporary storage space for each direction pair consisting of i and the opposite direction i, and the advection of the particle distribution functions is performed through pointer replacement between the array structure storage space and the temporary storage space .

In step S21, a partial array structure storage space is provided that includes first and second temporary storage spaces, respectively, for storing the particle distribution functions in direction i of all the nodes and the particle distribution functions in the opposite direction i '.

According to an embodiment, the partial array structure storage space can utilize the memory space used for temporal storage of the operation result in the conflict operation step.

In step S22, referring to the array structure storage space, a first particle distribution function stored in a storage position corresponding to the direction i of the first neighboring node opposite to the direction i ' 1 < / RTI > in the storage location of the node of interest within the temporary storage space.

In step S23, referring to the array structure storage space, a second particle distribution function stored in a storage position corresponding to the opposite direction i 'of the second neighbor node facing the direction i of the interested node is set in the opposite direction i' In the storage location of the node of interest within the second temporary storage space.

In step S24, the above-described steps S22 and S23 are repeated for all nodes in the array structure storage space.

In step S25, the pointer of the address range in which the particle distribution functions of direction i in the array structure storage space is stored is swapped with the address pointer of the first temporary storage space.

In step S26, the pointer of the address range in which the particle distribution functions in the opposite direction i 'in the array structure storage space are stored is swapped with the address pointer of the second temporary storage space.

At this time, if the address pointers of the first and second temporary storage spaces and the address pointers of the array structure storage space are interchanged in the above-described steps S25 and S26, the process proceeds to step S22 and step S24, And the addresses that were the second temporary storage spaces now belong to the array structure storage space with respect to direction i and the opposite direction i ', while steps S22 and S24 are repeated until the array < RTI ID = 0.0 > The addresses that were in the structure storage space now belong to the partial array structure storage space as the first and second temporary storage spaces for the next sequential arithmetic operation.

In step S27, the above-described steps (S22 to S26) are repeated for all directions i and i '.

The pseudo code for helping understanding of FIG. 2 is as follows.

는 방향 i의 입자 분포 함수들을 저장하기 위한 임시 저장 공간이고 (1)에서

는 각각의 노드

에 대해

에 해당하는 이웃 노드의 연산 결과

를

에 저장함을 의미한다.here,

Is the temporary storage space for storing the particle distribution functions of direction i and (1)

Lt; / RTI >

About

The operation result of the neighboring node corresponding to

To

.

는 반대 방향 i'의 입자 분포 함수들을 저장하기 위한 임시 저장 공간이고, (1)에서

는 각각의 노드

에 대해

에 해당하는 이웃 노드의 연산 결과

를

에 저장함을 의미한다.Likewise

Is a temporary storage space for storing the particle distribution functions of i 'in the opposite direction, and (1)

Lt; / RTI >

About

The operation result of the neighboring node corresponding to

To

.

에 대해 (1)에 수행되면, (3)에서, 임시 포인터

를 이용하여

의 포인터

과 방향 i의 직전 연산된 입자 분포 함수들이 저장된 어드레스 범위의 포인터

를 서로 교체하고 또한

의 포인터

과 반대 방향 i'의 직전 연산된 입자 분포 함수들이 저장된 어드레스 범위의 포인터

를 서로 교체할 수 있다.All nodes

(3), the temporary pointer < RTI ID = 0.0 >

Using

Pointer

And the pointers of the address ranges stored in the immediately preceding computed particle distribution functions of direction i

Lt; RTI ID = 0.0 >

Pointer

Lt; RTI ID = 0.0 > i < / RTI >

Can be exchanged with each other.

(1) - (3) have been completed for direction i and opposite direction i 'in (4), (1) - (3) are repeated for each of the remaining direction pairs.

3 is a diagrammatic illustration of an array structure storage space and a partial array structure storage space to be updated with respect to a specific direction in the advection step of the lattice Boltzmann technique based fluid numerical analysis method according to an embodiment of the present invention.

Referring to FIG. 3, when a grid-Boltzmann technique-based fluid numerical analysis method is implemented using the D2Q9 model, the particle distribution functions calculated at time t in the array structure storage space 31 are stored in each node, The stored state is illustrated schematically for each storage location.

Here, the particle distribution function is represented by a thin arrow, and the nodes are each of squares arranged in 3x3, and storage positions for directions are each indicated by hollow dashed arrows. The dashed arrows in the dashed dashed arrows illustrate how the particle distribution functions are stored before each advection is stored for each directional storage location at each node.

At the same time, the partial array structure storage space 32 of the partial array structure for storing the particle distribution functions in the horizontal two directions, i.e., the direction i from the right to the left, and the particle distribution functions in the left-to- It is also illustrated.

The partial array structure storage space 32 may be constituted by a first temporary storage space 321 and a second temporary storage space 322 in terms of a memory address actually, And the second temporary storage space 322 is a memory address range in which the particle distribution functions of the nodes are actually stored with respect to the opposite direction i '.

This makes it possible to copy the particle distribution functions to be spread from the neighbor nodes to the temporary storage space for each node of interest.

Referring now to FIG. 4, FIG. 4 is a flow chart illustrating a temporary storage of neighboring nodes of a node of interest in an array structure storage space in a particular direction, in a advection step of a method of fluid numerical analysis in accordance with an embodiment of the present invention. FIG. 3 is a diagram schematically illustrating a procedure of copying to a node of interest in space. FIG.

In order to propagate the particle distribution functions in the direction i and the opposite direction i 'of the interested node, the direction i of the first neighboring node and the direction i of the second neighboring node facing the opposite direction i' The particle distribution functions corresponding respectively to the opposite direction i 'should be moved to the respective storage locations of the direction i and the opposite direction i' of the interested node, respectively.

4, the storage location 411 of the direction i of the first neighboring node 41 facing the opposite direction i 'and direction i, respectively, about the central node of interest 40, The particle distribution functions respectively stored in the storage position 421 in the opposite direction i 'of the target node 42 should be moved to the storage locations 401 and 402 in the direction i and the opposite direction i' of the target node 40, respectively.

Thus, for updating the storage location 401 of direction i of the central node of interest 40, the direction i of the first neighboring node 41 facing the opposite direction i 'of the node of interest 40 The particle distribution function stored at the storage location 411 is copied to the storage location 331 for the direction i of the node 33 of the interested node 40 in the partial array structure storage space 32. [

The storage position 331 relating to the direction i of the node 33 in the partial array structure storage space 32 is actually provided in the first temporary storage space 321. [

Also for the update of the storage location 402 of the opposite direction i 'of the central node 40 of interest, the direction i of the second neighboring node 42, opposite to the direction i of the node 40 of interest, The particle distribution function stored in the storage location 421 is copied to the storage location 332 in the opposite direction i 'of the node 33 corresponding to the interested node 40 in the partial array structure storage space 32. [

The storage location 332 of the reverse direction i 'of the node 33 in the partial array structure storage space 32 is actually provided in the second temporary storage space 322. [

The storage positions of the radiated i and i ', which means the propagation of the particle distribution function, are represented by hollow solid arrows, and the copied particle distribution function is indicated by a thin solid line arrow.

Repeating this operation at all the remaining nodes results in the generation of the particle distribution functions stored in the storage locations of two horizontal directions i and i 'from the neighbor nodes of each node for all the nodes in the array structure storage space 31 Are respectively copied to the first and second temporary storage spaces 321 and 322 in the partial array structure storage space 32, respectively.

Referring now to FIG. 5, FIG. 5 is a flow chart of a method of analyzing fluid numerically based on a grid Boltzmann technique in accordance with an embodiment of the present invention. Referring to FIG. 5, Fig. 2 is a diagram schematically illustrating a procedure for updating by a user.

The partial array structure storage space 32 of FIG. 4, which is the immediately preceding state, stores particle distribution functions in which propagation is completed with respect to the direction i and the direction i 'opposite to the direction i. The contents of the partial array structure storage space 32 are shown in FIG. Rather than copying and overwriting again with respect to the corresponding direction i and the opposite direction i 'of the array structure storage space 31, the present invention achieves the same effect simply by replacing only those pointers in the memory address range in which such particle distribution functions are stored .

In FIG. 4, the storage locations corresponding to the direction i and the opposite direction i 'of each node in the partial array structure storage space 32 indicated by hollow hollow arrows are indicated by hollow dashed arrows in FIG. 5, The storage locations corresponding to the direction i and the opposite direction i 'of each node in the array structure storage space 31 indicated by hollow hollow arrows in FIG. 5 are indicated by hollow hollow arrows in FIG.

This implies that the horizontal particle distribution functions at each node are updated with the post-propagation particle distribution functions.

As for the remaining directions, the storage locations of each node are still represented by hollow dashed arrows, which means they are particle distribution functions before propagating between nodes.

6 is a block diagram illustrating a lattice Boltzmann technique based fluid numerical analysis apparatus in accordance with another embodiment of the present invention.

Referring to FIG. 6, the lattice Boltzmann technique-based fluid numerical analysis apparatus 60 of the present invention may include an impact computing unit 61, an advection memory control unit 62, and a memory 63.

The collision computing unit 61 computes the particle distribution functions for each of the nodes connected to each other in a plurality of directions on the basis of the lattice Boltzmann equation.

The calculation results of the particle distribution functions are stored in the memory 63 with a predetermined array structure. The memory 63 includes an array structure storage space 631 in which rows and columns are defined by directions and nodes and also stores the particle distribution functions of all the nodes by direction, A partial array structure storage space 632 for storing functions in at least one temporary storage space.

The advection memory control unit 62 controls the particle distribution function of the specific direction i stored in the array structure storage space 631 from the neighboring node opposed to the opposite direction i 'to the partial array structure storage space 632 by replacing the pointer of the address range in the array structure storage space 631 storing the particle distribution function of the specific direction i of the interested node as a pointer to the temporary storage space copied into the array structure storage space 631 Adjacent the particle distribution functions of the target node.

Herein, the opposite direction i 'indicates the opposite direction forming a straight line with the direction i.

More specifically, the advection memory control unit 62 may first create a temporary storage space 6321 in the partial array structure storage space 632 in the memory 63 to store the particle distribution functions of direction i of all the nodes.

Then, the advection memory control unit 62 stores the particle distribution function stored in the storage position of the direction i of the neighboring node opposite to the direction i 'of the direction i of the target node from the array structure storage space 631 to the partial array structure storage space To temporary storage 6321 of direction i, by storing in the storage location of the node of interest in temporal storage space 6321 in direction i within path 632, The particle distribution functions of all nodes can be stored.

Next, the advection memory control unit 62 stores the pointer of the address range in which the particle distribution functions of all nodes related to the direction i in the array structure storage space 631 are stored, the particle distribution functions in the temporary storage space 6321 related to the direction i It can be replaced by a pointer to an address range, and this operation can be repeated for each of all directions.

According to the embodiment, the advection memory control unit 62 comprises at least two sets of first and second temporary storage spaces 6321, 6322, respectively, for storing the particle distribution functions of all nodes with respect to at least two directions i and j The partial array structure storage space 632 can be created.

Next, referring to the array structure storage space 631, the advection memory control unit 62 controls the directions i and j of the neighboring nodes opposed to the opposite directions i 'and j' j is stored in storage locations of interest nodes in the first and second temporary storage spaces 6321 and 6322 for directions i and j, respectively, to all nodes < RTI ID = 0.0 > By storing in the first temporary storage space 6321 relating to the direction i the particle distribution functions of all the nodes adorned with respect to the direction i and also storing the particle distribution functions of the nodes in the second temporary storage space 6322 relating to the direction j in the direction j We can store the particle distribution functions of all nodes that are advected.

Next, the advection memory control unit 62 stores pointers of the address ranges in which the particle distribution functions of the entire nodes are stored in the array structure storage space 631 with respect to the directions i and j, respectively, to the first and second Can be replaced with pointers of address ranges in which particle distribution functions are stored in temporary storage spaces 6321 and 6322, respectively, and this operation can be repeated for each of the direction groups consisting of at least two directions.

At this time, the direction j may be the opposite direction i 'of the direction i.

In this case, specifically, the advection memory control unit 62 stores first and second temporary storage spaces 6321 and 6322, respectively, which can store the particle distribution functions of the interested node with respect to the direction i and the opposite direction i ' To generate a partial array structure storage space 632 that includes the partial array structure storage space 632.

Next, the adiabatic memory control unit 62 refers to the array structure storage space 631, and determines whether the first particle distribution stored in the storage location of direction i in the first neighboring node opposite to the direction i ' Stores the function in the storage location of the node of interest in the first temporary storage space 6321 with respect to direction i and stores the function in the storage location of the second node in the opposite direction i ' And store the particle distribution function in the storage location of the node of interest in the second temporary storage space 6322 for the opposite direction i '.

Next, the advection memory control unit 62 stores the pointer of the address range in which the particle distribution functions of all the nodes are stored in the array structure storage space 631 in the first temporary storage space 6321 related to the direction i, And a pointer in the address range in which the particle distribution functions of all the nodes are stored in the array structure storage space 631 in the opposite direction i 'is replaced with a pointer in the second temporary storage space Can be replaced by a pointer to an address range in which particle distribution functions are stored in a memory 6322 and this operation can be repeated for each of the remaining direction pairs configured in opposite directions.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. It will be understood that variations and specific embodiments which may occur to those skilled in the art are included within the scope of the present invention.

Further, the apparatus according to the present invention can be implemented as a computer-readable code on a computer-readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. Examples of the recording medium include ROM, RAM, optical disk, magnetic tape, floppy disk, hard disk, nonvolatile memory and the like. The computer-readable recording medium may also be distributed over a networked computer system so that computer readable code can be stored and executed in a distributed manner.

31 Array Architecture Storage Space
32 Partial Array Structure Storage Space
321 First temporary storage space
322 Second temporary storage space
40 Interested node
401 Storage location of direction i of interested node
402 Storage location of i 'in the opposite direction of the node of interest
41 first neighbor node
411 Storage location of direction i of first neighbor node
42 second neighbor node
421 Storage location in the opposite direction i 'of the second neighbor node
60 Grid Boltzmann technique based fluid numerical analysis device
61 collision computing unit
62 Ad Hoc Memory Controller
63 Memory
631 Array structure storage space
632 Partial array structure storage space
6321 First temporary storage space
6322 Second temporary storage space

Claims (20)

A computer-implemented lattice Boltzmann technique-based fluid numerical analysis method,
(a) computing, for each of the nodes connected to each other by the plurality of directions, the particle distribution functions for each direction based on the lattice Boltzmann equation; And
(b) in order to spread the particle distribution functions of each node to the neighbor nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the operation, By replacing the pointer of the address range in which the particle distribution function of the interested node in the specific direction i is stored as a pointer to the temporary storage space in which the particle distribution function in the specific direction i is copied and stored from the neighboring node facing the direction i ' Aliasing the particle distribution functions of the nodes with respect to the directions,
The step (b)
(b-1) generating a temporary storage space for storing the particle distribution functions of all the nodes with respect to the direction i;
(b-2) refers to the array structure storage space, and stores a particle distribution function stored in a storage position of a direction i of a neighboring node opposite to i 'in the opposite direction of the node of interest, Storing the particle distribution functions of all nodes with respect to direction i in the temporary storage space with respect to direction i by repeating the operation of storing the node in a storage location; And
(b-3) replacing the pointer of the address range in which the particle distribution functions of all nodes with respect to direction i in the array structure storage space are stored with a pointer of the address range in which the particle distribution functions are stored in the temporary storage space with respect to direction i And repeating the operation for each of all directions. ≪ RTI ID = 0.0 > 11. < / RTI > delete 2. The method of claim 1, wherein during one cycle of steps (b-1), (b-2) and (b-3), the direction i comprises at least two directions Numerical fluid analysis method. 2. The method of claim 1, wherein during one cycle of step (b-1), step (b-2) and step (b-3), direction i comprises two orientations orienting one another. Technique - based fluid numerical analysis method. The method according to claim 1,
Wherein the memory space required to provide the temporary storage space in step (b) is provided utilizing a memory space used for temporary storage of the computation results during step (a). Way. 6. The method of claim 5, wherein the temporary storage space in step (b) corresponds to an address range that belonged to the array structure storage space with respect to the specific direction and the opposite direction that was immediately preceded. Interpretation method. A computer-implemented lattice Boltzmann technique-based fluid numerical analysis method,
In order to spread the particle distribution functions of each node to the neighbor nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the collision calculation,
(i) providing a partial array structure storage space including first and second temporary storage spaces for storing the particle distribution functions in direction i of all nodes and the particle distribution functions in opposite direction i ', respectively;
(ii) a first particle distribution function stored in a storage location corresponding to a direction i of a first neighbor node facing the opposite direction i 'of the node of interest, with reference to the array structure storage space, Storing in a storage location of a node of interest in a temporary storage space;
(iii) a second particle distribution function stored in a storage location corresponding to the opposite direction i 'of the second neighbor node facing the direction i of the node of interest, with reference to the array structure storage space, Storing in a storage location of a node of interest in the second temporary storage space;
(iv) repeating steps (ii) through (iii) for all nodes in the array structure storage space;
(v) swapping a pointer of an address range in which particle distribution functions of direction i in the array structure storage space are stored with an address pointer of the first temporary storage space;
(vi) swapping a pointer of the address range in which the particle distribution functions in the opposite direction i 'in the array structure storage space are stored with an address pointer of the second temporary storage space; And
(vii) repeating steps (i) through (vi) for all orientations i and i 'in the opposite direction. 8. The method of claim 7, wherein the memory space required to provide the first and second temporary storage spaces in steps (i) through (vi) utilizes a memory space used for temporal storage of operation results during the conflict operation step Wherein the method comprises the steps of: 9. The method of claim 8, wherein the first and second temporary storage spaces provided in step (i) are stored in the array structure storage space with respect to a specific direction and an opposite direction during steps (v) and (vi) Wherein the first and second regions correspond to the address ranges to which they belong. A computer-readable recording medium containing a computer-readable program embodying a grid-Boltzmann technique-based fluid numerical analysis method performed by a computer according to any one of claims 1 to 3 to claim 9. A computer-implemented lattice Boltzmann technique-based fluid numerical analysis apparatus,
A collision computing unit for computing, for each of the nodes connected to each other by the plurality of directions, the particle distribution functions for each direction based on the lattice Boltzmann equation;
An array structure storage space in which rows and columns are defined by directions and nodes and which also stores particle distribution functions of all nodes by direction, and particle distribution functions of all nodes with respect to at least one specific direction into at least one temporary storage space A memory for providing a partial array structure storage space for storing the partial array structure storage space; And
In order to spread the particle distribution functions of the respective nodes in the array structure storage space according to the result of the operation to the neighboring nodes, a specific direction i from the neighboring node facing the opposite direction i ' By replacing the pointer of the address range in which the particle distribution function of the interested node in the specific direction i is stored with the pointer indicating the temporary storage space in which the particle distribution function of the node i is copied and stored, And a control unit
Wherein the advection memory control unit comprises:
(c-1) generating, in the memory, the temporary storage space for storing the particle distribution functions of all nodes with respect to direction i,
(c-2) referring to the array structure storage space, a particle distribution function stored in a storage location of a direction i of a neighboring node opposite to i 'in the opposite direction of the node of interest, Storing the particle distribution functions of all the nodes in the direction i in the temporary storage space with respect to the direction i by repeating the operation of storing the node in the storage location,
(c-3) replacing the pointer of the address range in which the particle distribution functions of all nodes with respect to direction i in the array structure storage space are stored with a pointer of the address range in which the particle distribution functions are stored in the temporary storage space with respect to direction i And to repeat the operation for each of all directions. ≪ RTI ID = 0.0 > 8. < / RTI > delete The method according to claim 11, wherein, while the advection memory controller performs one cycle of (c-1) operation, (c-2) operation and (c-3) operation, direction i includes at least two directions Lattice Boltzmann technique based fluid numerical analysis device characterized. 12. The method of claim 11, wherein the advection memory controller includes two directions that orient to one another during one cycle of (c-1), (c-2) Wherein the first and second sets of data are based on a grid-Boltzmann technique. 12. The method of claim 11 wherein the memory space required to provide the temporary storage space in the memory is provided utilizing the memory space utilized by the conflict operation part for temporal storage of the computation results. Numerical analysis apparatus. 16. The method of claim 15, wherein the temporary storage space provided in the memory corresponds to an address range that was within the array structure storage space with respect to a particular direction and the opposite direction imposed immediately before. Device. A computer-implemented lattice Boltzmann technique-based fluid numerical analysis apparatus,
A collision computing unit for computing, for each of the nodes connected to each other by the plurality of directions, the particle distribution functions for each direction based on the lattice Boltzmann equation;
An array structure storage space in which rows and columns are defined by directions and nodes and also stores particle distribution functions of all the nodes in a direction and a particle array storage space in which all particle distribution functions of all nodes in a specific direction and a reverse direction are stored in two temporary storage spaces A memory for providing a partial array structure storage space for storing in a memory; And
And an advection memory control unit for diffusing the particle distribution functions of each node into neighboring nodes in the array structure storage space storing the particle distribution functions of the nodes according to the result of the collision calculation,
Wherein the advection memory control unit comprises:
(i) providing, in the memory, a partial array structure storage space including first and second temporary storage spaces for respectively storing particle distribution functions in direction i of all nodes and particle distribution functions in opposite direction i '
(ii) a first particle distribution function stored in a storage location corresponding to a direction i of a first neighbor node facing the opposite direction i 'of the node of interest, with reference to the array structure storage space, Storing in a storage location of a node of interest in the temporary storage space,
(iii) a second particle distribution function stored in a storage location corresponding to the opposite direction i 'of the second neighbor node facing the direction i of the node of interest, with reference to the array structure storage space, Storing at a storage location of a node of interest in the second temporary storage space,
(iv) repeating steps (ii) to (iii) for all nodes in the array structure storage space,
(v) swapping a pointer of an address range in which the particle distribution functions of direction i in the array structure storage space are stored with an address pointer of the first temporary storage space,
(vi) swapping a pointer of the address range in which the particle distribution functions in the opposite direction i 'in the array structure storage space are stored with the address pointer of the second temporary storage space, and
(vii) repeating steps (i) through (vi) for all directions i and i 'in the opposite direction. 18. The method of claim 17, wherein the memory space required to provide the first and second temporary storage spaces in steps (i) through (vi) utilizes a memory space used for temporal storage of operation results during the conflict operation step Wherein the first and second regions are provided by a lattice Boltzmann technique. 19. The method of claim 18, wherein the first and second temporary storage spaces provided in step (i) are within the array structure storage space with respect to a specific direction and an opposite direction during steps (v) and (vi) Wherein the first and second regions correspond to the address ranges to which they belong. delete

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