KR100972624B1 - Apparatus and method for simulating multiphase fluids - Google Patents

Abstract

PURPOSE: An apparatus and a method for simulating multiphase fluids are provided to express a natural multi-phase fluid by applying a calculated temporary level set value for each node of a cell. CONSTITUTION: A background fluid forming unit(110) forms a ground fluid, and the background fluid is expressed through a grid structure. A fluid particle forming unit(120) forms fluid particles inside at least one cell of a grid structure. A level set calculator(130) calculates a temporary level set value for each node of the grid structure. If at least one cell is included in a fluid particle group, a level set applying unit(140) applies the temporary level set value for each node of the grid structure.

Description

Apparatus and method for simulating multiphase fluids

TECHNICAL FIELD The present invention relates to a multiphase fluid simulation apparatus and method, and more particularly, to an apparatus and method capable of computer graphics of a large fluid mass including small fluid particles.

The technique of understanding and simulating the disordered movement of bubbles within multiphase fluids such as carbonated water is not only applied in engineering fields including ship hydrodynamics or reactor cooling, but also in the visual realism of computer graphics. Is a necessary skill to increase. Therefore, researches on physics-based fluid simulation techniques promoted by computational fluid dynamics to express more realistic bubbles or bubbles have been conducted in various fields.

The basis of the fluid simulation is the Navier-Stokes equation. This equation is a rewrite of Newton's equation of motion, F = ma, for fluids and represents the relationship between fluid acceleration, force from fluid movement, pressure, external forces, and fluid viscosity. Since the Navier-Stokes equations are defined in continuous space, two calculation methods are used to calculate them in a computer.

First, the grid-based method is a simulation method based on Eulerian grids, which divides the space into uniform grids and calculates the fluid properties at each grid point. A brid-based solver can handle large chunks of fluid, such as liquids and gases, effectively and accurately, making them ideal for smoother sleep.

Particle-based method, on the other hand, is a technique that obtains the final shape of a fluid by expressing the fluid as a number of particles exerting force on each other based on Lagrangian particles and tracking the movement of the particles. Has the advantage of calculating the violent movements. Particle-based systems based on smooth particle hydrodynamics (SPH) are more resilient and easier to handle when focused on small-scale details.

As such, the lattice-based and particle-based methods are complementary to fluid simulation techniques, which are suitable for describing different types of fluids. The combination of these two makes it possible to more realistically represent polyphase fluids containing small fluid particles. In other words, the oily lattice is used to represent a liquid or gaseous mass as a background, and details of bubbles small enough to be processed by the lattice are made using SPH particles.

However, when the small fluid particles are simulated by particle-based methods, the force applied to each particle such as cohesion force can be large enough to combine several particles into a large mass and be processed by the lattice. . Even in this case, using the same particle-based method, the fluid representation becomes less realistic. Therefore, there is a need to present a simulation technique that can solve these problems.

An object of the present invention is to provide a multi-phase fluid simulation apparatus and method capable of naturally expressing a multi-phase fluid composed of a plurality of fluid shapes using a lattice-based method and a particle-based method.

Another technical problem to be solved by the present invention is a computer-readable program for executing a multi-phase fluid simulation method that can naturally express a multi-phase fluid composed of a plurality of fluid shapes using a lattice-based method and a particle-based method. To provide a record carrier.

In order to achieve the above technical problem, the multi-phase fluid simulation apparatus according to the present invention, a background fluid forming unit for forming a background fluid by a grid structure that divides the three-dimensional space; A fluid particle forming unit for forming a fluid particle in a cell defined by the lattice structure; A level set calculator for calculating a temporary level set value for each node corresponding to each vertex of the cell based on the physical quantity of the fluid particle; And a level set that applies the temporary level set value as a node value to each node of a cell in which the fluid particles constituting the fluid particle population are located when the fluid particles are formed by agglomeration of the fluid particles. Applicable portion;

In order to achieve the above technical problem, the multiphase fluid simulation method according to the present invention comprises: a background fluid forming step of forming a background fluid by a lattice structure dividing a three-dimensional space; Forming a fluid particle in a cell defined by the lattice structure; A level set calculation step of calculating a temporary level set value for each node corresponding to each vertex of the cell based on the physical quantity of the fluid particle; And a level set that applies the temporary level set value as a node value to each node of a cell in which the fluid particles constituting the fluid particle population are located when the fluid particles are formed by agglomeration of the fluid particles. Has an application step.

According to the multiphase fluid simulation apparatus and method according to the present invention, in a multiphase fluid including a background fluid formed by a lattice structure and a fluid particle formed by a particle-based method, a fluid particle group generated by agglomeration of fluid particles into a cell of a lattice structure is formed. If it is larger than the size, by applying the temporary level set value calculated for each node of the cell, it is possible to express the shape of the natural polyphase fluid while reducing the additional calculation cost.

Hereinafter, exemplary embodiments of a multiphase fluid simulation apparatus and method according to the present invention will be described in detail with reference to the accompanying drawings.

1 is a block diagram showing the configuration of a preferred embodiment of a multiphase fluid simulation apparatus according to the present invention.

Referring to FIG. 1, the multi-phase fluid simulation apparatus according to the present invention includes a background fluid forming unit 110, a fluid particle forming unit 120, a level set calculating unit 130, and a level set applying unit 140. .

The background fluid forming unit 110 forms a background fluid by a lattice structure dividing a three-dimensional space.

The movement of the background part of a polyphase fluid, ie, large chunks of water or air (hereafter background fluid), is carried out by a grid-based method using a grid structure consisting of cells that divide the three-dimensional space uniformly or unevenly. Is expressed. Therefore, a grid structure must be created to represent the background fluid. As one kind of such a lattice structure, a background fluid can be expressed by using an octree lattice structure in which a cell size is expressed in a plurality of stages. In the grid-based method, the background fluid is expressed based on the velocity calculated for the entire background fluid regardless of its position in the background fluid.

The Navier-Stokes equations of Equations 1 and 2 express the movement of the background fluid which is incompressible.

={u,v,w}는 속도벡터, ρ는 밀도, p는 압력, 그리고

는 중력 및 부력을 비롯한 외부힘을 나타내는 벡터이다.here,

= {u, v, w} is the velocity vector, ρ is the density, p is the pressure, and

Is a vector representing external forces, including gravity and buoyancy.

라 하고, 이를 이용하여 수학식 1을 다음의 수학식 3과 수학식 4에 나타난 두 개의 방정식으로 나눈다.The solution of the Navier-Stokes equation can be obtained by the projection method using the finite-difference method proposed by Chorin. In addition, the solution of Equations 1 and 2 is performed while updating the velocity of the background fluid from u ⁿ to u ^{n + 1} for Δt in the nth time step. First, the medium velocity of the background fluid

The equation 1 is divided into two equations shown in Equations 3 and 4 below.

={u,v,w}는 속도벡터, t는 시간, ρ는 밀도, p는 압력, 그리고

는 중력 및 부력을 비롯한 외부힘을 나타내는 벡터이다.here,

= {u, v, w} is the velocity vector, t is time, ρ is density, p is pressure, and

Is a vector representing external forces, including gravity and buoyancy.

으로부터 중간속도인

를 구하기 위해 준 라그랑즈 방법(semi-Lagrangian method)을 사용하여 이류(advection)항인

을 계산하고, 양의 유한차분 또는 음의 가변점도 형성(implicit variable viscosity formulation)에 의해 점도항인

을 계산한다.

Medium speed from

The advection term using the semi-Lagrangian method to find

And calculate the viscosity term by positive finite difference or negative variable viscosity formulation.

.

로부터 최종속도인

을 결정하는 것이다. 발산(divergence)식인 수학식 4는 다음의 수학식 5와 같이 프아송(Poisson) 식의 형 태로 나타낼 수 있다.The final step is

Final velocity from

To decide. Equation 4, which is a divergence equation, may be expressed in the form of Poisson equation, as shown in Equation 5 below.

={u,v,w}는 속도벡터이다.Where p is pressure, ρ is density, t is time, and

= {u, v, w} is the velocity vector.

은 0이 되어야 한다. 위 수학식 5를 풀이하면 압력 프로필(profile)을 결정할 수 있으며, 배경유체의 최종속도는 다음 수학식 6에 의해 결정된다.According to Equation 2,

Must be zero. Solving Equation 5 above, the pressure profile can be determined, and the final velocity of the background fluid is determined by Equation 6 below.

은 배경유체의 최종속도, p는 압력, ρ는 밀도, t는 시간, 그리고

={u,v,w}는 속도벡터이다.here,

Is the final velocity of the background fluid, p is the pressure, ρ is the density, t is the time, and

= {u, v, w} is the velocity vector.

By solving the Navier-Stokes equation as above, the velocity of the background fluid can be expressed to express the motion of the background fluid, which is a large mass in the multiphase fluid. In addition, the octree lattice structure is used to represent the interface between the fluids, and the back and forth error compensation and correction (BFECC) method can be additionally used to reduce the volume loss and guarantee the secondary accuracy. Think of the surface as an equilateral surface of a function that changes over time, instead of directly tracking the surface, the level set method, a numerical method of tracking a function, and a virtual particle representing a point inside or outside the fluid. As a result, the particle level set method, which combines a method of tracking the free boundary of the fluid using particles moving along the flow of the fluid, can smoothly express the interface of the fluid.

In the particle level set method, a marker particle formed to be adjacent to an interface of the fluid is used to express the interface of the fluid. For marker particles, water is corrected when φ, which is the value of the distance function used in the levelset method, is negative, and air is positive. At this time, if there are marker particles whose sign is opposite to the φ value of the background fluid, such as bubbled water, these particles are represented as escaped particles. Based on this, fluid particles are simulated as described below.

The fluid particle forming unit 120 forms fluid particles in a cell defined by a lattice structure. In this case, the fluid particles cannot be represented by the lattice-based method, so they are represented by the particle-based method. As an example, the fluid particles may be formed to be 0.3 to 0.8 times the cell size.

의 합에 의해 다음의 수학식 7로 결정된다.In particle-based methods, the acceleration of each fluid particle is the force exerted by adjacent fluid particles.

By the sum, it is determined by the following equation (7).

는 복수의 유체입자들 중에서 유체입자 i의 가속벡터,

는 인접한 유체입자들에 의해 입자 i에 가해지는 힘, 그리고 ρ_i는 유체입자 i의 밀도이다.here,

Is the acceleration vector of fluid particle i,

Is the force exerted on the particle i by adjacent fluid particles, and ρ _i is the density of the fluid particle i.

In addition, the density of the fluid particle i ρ _i is expressed as Equation (8) for.

은 반경이 r인 방사대칭 커널함수이다.Where ρ _i is the density of fluid particle i, m _i is the mass of fluid particle i, and

Is a radially symmetric kernel function with radius r.

The velocity and position of the fluid particles can be determined by Euler's integration shown in Equations 9 and 10, respectively. Using the Euler method, the position of the fluid particles in the background fluid is determined indirectly by velocity.

는 유체입자 i의 속도,

는 유체입자 i의 가속도,

는 유체입자 i의 위치, 그리고 Δt는 시간간격이다.here,

Is the velocity of fluid particle i,

Is the acceleration of fluid particle i,

Is the position of the fluid particle i, and Δt is the time interval.

에 대한 스칼라 필드값인

는 다음의 수학식 11에 의해 인접하는 유체입자에 대한 물리량의 가중 합(weighted sum)을 산출함으로써 보간된다.The force exerted from adjacent fluid particles can be found using pressure. According to SPH, the position of fluid particle i

Scalar field value for

Is interpolated by calculating the weighted sum of physical quantities for adjacent fluid particles by the following equation (11).

는 유체 내의

위치에 대한 필드값, m_j는 유체입자 j의 질량, ρ_j는 유체입자 j의 밀도,

은 반경이 h인 스무딩 커널,

는 유체입자 i와 유체입자 j 사이의 벡터, 그리고 A_j는

에서의 필드값이다. 또한 커널 함수인

는

의 식을 만족시킴으로써 정규화된다.here,

Is within the fluid

Field value for position, m _j is the mass of fluid particle j, ρ _j is the density of fluid particle j,

Is a smoothing kernel with radius h,

Is the vector between fluid particle i and fluid particle j, and A _j is

Field value at. Also a kernel function

Is

Normalized by satisfying

When the force applied from the fluid particle j to the fluid particle i is calculated using Equation 11 above, it is expressed as Equation 12 below.

은 반경이 r인 스무딩 커널, 그리고

이다. 또한 질량 m_i는 r_i ³에 비례한다.Where V _i is the volume of fluid particle i, m _i / ρ _i , V _j is the volume of fluid particle j, P _i is the pressure of fluid particle i expressed as kρ _i by the control parameter k, P _j is Pressure of fluid particle j,

Is a smoothing kernel with radius r, and

to be. The mass m _i is also proportional to r _i ³ .

In general, SPH systems are highly dependent on viscosity. This is to improve the stability when representing large chunks of fluid. However, in the present invention, a lattice-based method is used for expressing a large mass of background fluid, and SPH is used only for expressing small fluid particles, and thus a force related to viscosity can be omitted.

2 illustrates an example of a background fluid formed by the background fluid forming unit 110 and a fluid particle formed by the fluid particle forming unit 120. 2, a large liquid mass is represented by a lattice structure composed of cells of various sizes, and bubbles generated in the liquid are represented by SPH particles.

The simulation method described above represents a background fluid and a fluid particle. In order to simulate polyphase fluids, the background fluid and the fluid particles must be represented together. In this case, the background fluid and the fluid particles have different properties (volume, density, velocity, etc.) and thus affect each other.

First, in a multiphase fluid, drag force and lift may act on small fluid particles by a large mass of background fluid. Drag and lift are expressed by Equations 13 and 14, respectively.

는 유체입자에 작용하는 항력, k_drag는 항력계수, r_i는 반경,

는 유체입자의 속도, 그리고

는 배경유체의 속도이다.here,

Is the drag acting on the fluid particle, k _drag is the drag coefficient, r _i is the radius,

Is the velocity of the fluid particle, and

Is the speed of the background fluid.

는 유체입자에 작용하는 양력,k_lift는 양력계수, V_i는 유체입자의 부피,

는 유체입자의 속도,

는 배경유체의 속도, 그리고 ω_i는 소용돌이도(vorticity)로서

에 의해 산출된다.here,

Is the lift acting on the fluid particle, k _lift is the lift coefficient, V _i is the volume of the fluid particle,

Is the velocity of the fluid particle,

Is the velocity of the background fluid, and ω _i is the vorticity

Calculated by

The above drag and lift are added to the right side of the Navier-Stokes equation of Equation 1 at each time step to affect the motion of the background fluid.

In order to express the motion of fluid particles in more detail, the vorticity confinement can be introduced in the above-described SPH technique. First, the vorticity at the mass center between two fluid particles is calculated. The center of mass is represented by Equation 15, and the vortex degree at the center of mass is represented by Equation 16.

는 다상유체 내에서 유체입자 i와 유체입자 j 사이의 질량중심 의 위치, m_i는 유체입자 i의 질량, m_j는 유체입자 j의 질량,

는 유체입자 i의 위치, 그리고

는 유체입자 j의 위치이다.here,

Is the location of the center of mass between fluid particle i and j in the multiphase fluid, m _i is the mass of fluid particle i, m _j is the mass of fluid particle j,

Is the position of fluid particle i, and

Is the position of the fluid particle j.

는 유체입자의 속도이다.Where ω is the vortex degree, and

Is the velocity of the fluid particle.

Next, the vorticity location vector is represented by Equation 17 below.

는 유체입자 i와 유체입자 j 사이의 질량중심, 그리고

는 유체입자 i의 위치이다.Where η is the vortex degree position vector,

Is the center of mass between fluid particle i and fluid particle j, and

Is the position of the fluid particle i.

Using the equations (15) to (17), the confinement force of the vorticity acting on the fluid particles can be expressed by the following equation (18).

는 구속력, ε은 상수, ω는 소용돌이도, ρ_i는 유체입자 i의 밀도, 그리고

은 일반화된 소용돌이도 위치벡터, 즉

이다.here,

Is the binding force, ε is the constant, ω is the vortex degree, ρ _i is the density of the fluid particle i, and

Is a generalized vortex position vector,

to be.

This binding force causes the SPH system of fluid particles to diverge, so the generalized vorticity is used in Equation (18).

In addition, when the polyphase fluid to be represented by the polyphase fluid simulation apparatus according to the present invention represents bubbles generated in the water, that is, when the background fluid is water and the fluid particles are air, the density of water is greater than that of air. The particles tend to clump together quickly. This is due to the cohesive attraction force acting between the fluid particles, expressed by Equation 19 below.

은 유체입자 i와 유체입자 j 사이에서 작용하는 응집력, k_attraction은 비례계수, W_attraction은 유체입자 사이의 압력의 균형을 맞추어 위와 같은 힘을 용이하게 정할 수 있도록 하는 상수,

는 유체입자 i와 유체입자 j 사이의 위치벡터를 사용하여

와 같이 나타내어지는 벡터, r_i와 r_j는 각각 유체입자 i와 유체입자 j의 반경, 그리고 ρ_i는 유체입자 i의 밀도이다.here,

Is the cohesive force acting between the fluid particle i and the fluid particle j, k _attraction is the proportional coefficient, W _attraction is a constant that makes it easy to determine the above forces by balancing the pressure between the fluid particles,

Uses the position vector between fluid particle i and fluid particle j

Where r _i and r _j are the radii of fluid particle i and j, and ρ _i is the density of fluid particle i, respectively.

When the density of the fluid particles is increased due to the cohesive force, the adjacent fluid particles are pushed out from each other by the pressure between the fluid particles represented by Equation 12. W _attraction , a constant used in Equation 19, was introduced to stabilize the phenomenon and easily obtain cohesion.

The small fluid particles aggregate with each other by the binding force shown in Equation 18 and the cohesion shown in Equation 19. Large fluid particle populations that are larger than the size of the lattice used in the lattice-based method due to aggregation of small fluid particles can be sufficiently represented by the lattice-based method. Therefore, when the small fluid particles represented by the particle-based method aggregate to each other to form a large fluid particle population, it is preferable to express it again by the lattice-based method.

To this end, the level set calculator 130 calculates a temporary level set value for each node corresponding to each vertex of the cell constituting the lattice structure based on the physical quantity of the fluid particles.

Physical quantities of fluid particles that affect temporary levelset values include mass, volume, and the like. The temporary levelset value is also affected by the smoothing kernel acting on that node. The level set calculator 130 calculates a temporary level set value expressed by Equation 20 for each node and stores the temporary level set value for each node in a separate storage device (not shown) or a memory provided by itself.

는 격자구조의 i번째 노드에 부여되는 레벨셋 값, m은 질량계 수, V_j는 유체입자 j의 부피, 그리고 W(x_ij,r_j)는 수학식 8에 나타난 것과 동일한 커널함수이다.here,

Is the level set value assigned to the i-th node of the lattice structure, m is the mass coefficient, V _j is the volume of the fluid particle j, and W (x _ij , r _j ) is the same kernel function as shown in Equation (8).

When the level set calculator 130 calculates the temporary level set value, it is preferable to set the range of the fluid particles so that the temporary level set value of the corresponding node is not affected by the physical quantity of the fluid particles deviating from the node. . As an example, one large cell composed of a plurality of cells sharing a node to calculate a temporary level set value and configured to neighbor each other is defined as a reference cell for calculating a temporary level set value, and a reference corresponding to each node. The temporary level set value may be calculated based on the physical quantities of the fluid particles located in the cell. 3 is a diagram illustrating a reference cell composed of eight cells configured to share one node N and neighbor each other. In the case of FIG. 3, all of the eight cells forming the reference cell are the same. However, when the octree lattice structure is used, the cells forming the reference cell may have different sizes. In this case as well, the reference cell may be formed by cells sharing the corresponding nodes and located adjacent to each other to calculate a temporary level set value.

 At this time, since the moving speed or direction changes with time, the background fluid and the fluid particles also need to be calculated and updated in real time with time. In addition, when the temporary level set value is calculated for all nodes of the grid structure, the number of calculations to be performed increases, so that the fluid particles inside the reference cell corresponding to the node for which the temporary level set value is calculated to improve the performance of the system. Only when is located, can you make a temporary levelset for that node. The temporary level set value calculated for the node where the fluid particles are not located in the reference cell is zero.

4 is a plan view showing a background fluid formed by a lattice structure composed of a plurality of cells and a polyphase fluid represented by fluid particles formed inside each cell.

Referring to Figure 4, (1,1) to (5,5) represents each node of the lattice structure, the circular fluid particles are formed inside the cell defined by the lattice structure. At this time, the level set calculator 130 searches for each node to calculate a temporary level set value. The temporary level set calculated by Equation 20 when at least one fluid particle is located in a reference cell (four cells sharing one node in FIG. 3) corresponding to the node for which the temporary level set value is to be calculated. The value will be nonzero. However, if the reference cell does not contain fluid particles, such as nodes (4, 2), the temporary level set calculated for that node is zero.

When the at least one cell is included in the fluid particle population formed by agglomeration of the fluid particles with each other, the level set applying unit 140 sets a temporary level set value as a node value at each node of the cell where the fluid particles constituting the fluid particle population are located. Apply.

As described above, the particle-based method is used to express a fluid that cannot be represented by the size of the lattice, so that the fluid particles form a population so that the fluid particle population becomes larger than the size of one cell and thus the size of the lattice. If possible, it is not desirable to continue to represent the population of fluid particles by particle-based methods. Therefore, the level set applying unit 140 uses the temporary level set value calculated by the level set calculating unit 130 to express the fluid particle population larger than the size of the cell by the lattice-based method. That is, the temporary level set value calculated for the node is applied to each node of the cell where the fluid particles constituting the fluid particle group are located among the temporary level set values calculated and stored for each node of the lattice structure. This results in a fluid particle population represented by a lattice based method.

In this way, the particles smaller than the lattice size are expressed using the particle-based method, and the lattice and lower lattice is expressed by using the lattice-based method for the fluid particle population or the background fluid that is large enough to be expressed by the lattice structure. It is possible to effectively simulate polyphase fluids in each sub-grid region.

FIG. 5 is a diagram illustrating a case in which a plurality of fluid particles are aggregated to form a fluid particle population in the multiphase fluid shown in FIG. 4.

Referring to FIG. 5, fluid particles move with the flow of the background fluid and aggregate by cohesion to form a large fluid particle population. The formed fluid particle population contains one cell. Therefore, since this can be expressed by a grid-based method, the level set applying unit 140 applies a temporary level set value calculated for the node to each node of a cell in which the fluid particles constituting the fluid particle group are located. In this case, nodes (2,3), (2,4), (3,3) and (3,4) included in the fluid particle population or nodes (2,5) and (2,5) containing a large number of fluid particles in a cell ( 3,5) and the like are greatly affected by the aggregation of fluid particles. However, if the number of fluid particles located inside the cell including the node is small, such as nodes (3,2), (4,2), and (4,3), the fluid particles are not affected by aggregation. .

Figure 6 is a flow chart showing the implementation of a preferred embodiment of the multiphase fluid simulation method according to the present invention.

Referring to FIG. 6, the background fluid forming unit 110 forms a background fluid by a grid structure dividing a three-dimensional space (S610). Next, the fluid particle forming unit 120 forms the fluid particles in the cell defined in the grid structure (S620). The level set calculator 130 calculates a temporary level set value for each node corresponding to each vertex of the cell constituting the lattice structure based on the physical quantity of the fluid particle (S630). In this case, the temporary level set value may be calculated based on the physical quantity of the fluid particles located in the reference cell including a plurality of cells formed adjacent to each other including the corresponding node.

When the fluid particles aggregate with each other to form a large fluid particle population, and at least one cell is included in the formed fluid particle population (S640), the level set applying unit 140 positions the fluid particles constituting the fluid particle population. The temporary level set value calculated by the level set calculating unit 130 is applied to each node of the cell as the node value (S650).

In order to evaluate the performance of the multiphase fluid simulation apparatus and method according to the present invention, an experiment was performed to simulate the polyphase fluid by computer programming. The experiment was performed on an Intel Core2 CPU 3.0GHz, and the image generated by the simulation was rendered by ray-tracing. In addition, all simulations used the level set method and the back and forth error compensation and correction (BFECC) method in the octree lattice structure with the maximum level of 7. In addition, when the SPH method is applied, the radius of the particles has a value of 0.3 to 0.8 times the lattice size of the lattice structure.

FIG. 6 and FIG. 7 show comparisons of the case represented by the level set when the air bubbles in the water are expressed only by the particle-based method and when the air bubbles are aggregated together. 6 and 7 illustrate a case where air bubbles are expressed only as particles by rendering particles as they are. On the other hand, the right side of FIGS. 6 and 7 shows a case in which a large set of bubbles is expressed by applying a level set to the bubbles combined with each other. The level set is applied to the fluid particles larger than the lattice size, and as a result, the fluid particles are represented by the lattice structure, thereby enabling more accurate simulation. Especially in the case of severe turbulent water, many of these cases occur, so that the multiphase fluid simulation apparatus and method according to the present invention can be effectively applied.

FIG. 8 is a diagram illustrating an example in which water is poured on one wall of an empty box to simulate the flow of highly turbulent water. The fluid particles produced by the simulation of FIG. 8 are all 39.435. At this time, the fluid particles located in the lower right part of FIG. 8 are fluid particles larger than the lattice size and are expressed by applying a level set value. When applying the level set value to the fluid particles represented by the particle-based method, it is possible to express natural bubble movement without requiring a large calculation cost.

The invention can also be embodied as computer readable code on a computer readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored. Examples of the computer-readable recording medium include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like, and may be implemented in the form of a carrier wave (for example, transmission via the Internet) . The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.

Although the preferred embodiments of the present invention have been shown and described above, the present invention is not limited to the specific preferred embodiments described above, and the present invention belongs to the present invention without departing from the gist of the present invention as claimed in the claims. Various modifications can be made by those skilled in the art, and such changes are within the scope of the claims.

1 is a block diagram showing the configuration of a preferred embodiment of a multiphase fluid simulation apparatus according to the present invention;

2 is a view showing an example of a background fluid formed by the background fluid forming unit 110 and a fluid particle formed by the fluid particle forming unit 120,

3 illustrates a reference cell consisting of eight cells configured to share one node N and neighbor each other;

4 is a plan view showing a multi-phase fluid represented by a background fluid formed by a lattice structure composed of a plurality of cells and fluid particles formed inside each cell;

FIG. 5 illustrates a case where a plurality of fluid particles are aggregated to form a fluid particle population in the multiphase fluid shown in FIG. 3;

6 is a flow chart showing the performance of a preferred embodiment of the multiphase fluid simulation method according to the present invention;

7 and 8 are views comparing the case represented by the level set when the air bubbles in the water are represented only by the particle-based method and the air bubbles are agglomerated with each other, and,

FIG. 9 is a diagram illustrating an example in which water is poured on one wall of an empty box to simulate the flow of highly turbulent water.

Claims (17)

A background fluid forming unit forming a background fluid represented by a lattice structure dividing a three-dimensional space by a plurality of cells; A fluid particle forming unit for forming fluid particles in at least one cell of a lattice structure representing the background fluid; A level set calculator configured to calculate a temporary level set value for each node of the lattice structure corresponding to a vertex of each cell constituting the lattice structure based on a physical quantity of the fluid particle; And The temporary level set value for the node of the lattice structure corresponding to each vertex of the cell where the fluid particles constituting the fluid particle population are located when the fluid particles are included in the fluid particle population formed by aggregation of the fluid particles. A multi-phase fluid simulation apparatus comprising a; level set applying unit for applying a node value. The method of claim 1, And the lattice structure is an octree lattice structure in which the size of the cell is expressed in a plurality of steps. The method according to claim 1 or 2, The fluid particle forming unit is a multi-phase fluid simulation device, characterized in that for forming the fluid particles so that the radius of the fluid particles is 0.3 ~ 0.8 times the size of the cell. The method according to claim 1 or 2, And the level set calculating unit calculates the temporary level set value when the fluid particles are present in a reference cell including a plurality of cells sharing the nodes and neighboring each other. The method according to claim 1 or 2, The level set calculating unit calculates a temporary level set value represented by the following formula A: Equation A

Is the temporary level set value given to the i-th node of the lattice structure, m is the mass coefficient, V _j is the volume of the fluid particle j among the fluid particles, and W (x _ij , r _j ) is the fluid particle j Radial symmetric kernel function with radius equal to radius. The method according to claim 1 or 2, The fluid particle forming unit forms the fluid particles such that a drag force represented by Equation B and a lift force represented by Equation C act on the fluid particles. Device: Equation B

here,

Is the drag acting on the fluid particle, k _drag is the drag coefficient, r _i is the radius of the fluid particle,

Is the velocity of the fluid particle, and

Is the speed of the background fluid. Equation C

here,

Is the _lift force acting on the fluid particles, k _lift is the lift coefficient, V _i is the volume of the fluid particles,

Is the velocity of the fluid particles,

Is the velocity of the background fluid, and ω _i is the vorticity

Calculated by The method according to claim 1 or 2, Wherein the fluid particle forming unit forms the fluid particles such that a vorticity confinement force represented by Equation (D) is applied to the fluid particles: [Equation D]

here,

Is the restraining force, ε is a preset proportional constant, ω is the vortex of the fluid particles, ρ _i is the density of fluid particles i, and

Is a generalized vortex position vector,

to be. The method according to claim 1 or 2, The fluid particles are a multi-phase fluid simulation apparatus characterized in that the aggregation by the cohesion force represented by the following equation E to form the fluid particle population: [Equation E]

here,

Is the cohesion force acting between the fluid particle i and the fluid particle j, k _attraction is the proportional coefficient, W _attraction is a constant to easily determine the cohesion force by balancing the pressure between the fluid particles,

Uses the position vector between fluid particle i and fluid particle j

Where r _i and r _j are the radii of fluid particle i and j, and ρ _i is the density of fluid particle i, respectively. A background fluid forming step of forming a background fluid represented by a lattice structure dividing a three-dimensional space by a plurality of cells; Forming a fluid particle in at least one cell of a lattice structure representing the background fluid; A level set calculation step of calculating a temporary level set value for each node of the lattice structure corresponding to a vertex of each cell constituting the lattice structure based on a physical quantity of the fluid particle; And The temporary level set value for the node of the lattice structure corresponding to each vertex of the cell where the fluid particles constituting the fluid particle population are located when the fluid particles are included in the fluid particle population formed by aggregation of the fluid particles. A multi-phase fluid simulation method comprising a; applying a level set to the node value. The method of claim 9, And the lattice structure is an octree lattice structure in which the size of the cell is expressed in a plurality of steps. The method according to claim 9 or 10, In the fluid particle forming step, wherein the fluid particles to form the fluid particles so that the radius of the fluid particles is 0.3 ~ 0.8 times the size of the cell. The method according to claim 9 or 10, And in the level set calculating step, calculating the temporary level value when the fluid particles are present in a reference cell composed of a plurality of cells sharing the nodes and neighboring each other. The method according to claim 9 or 10, In the level set calculation step, a multi-phase fluid simulation method characterized in that for calculating a temporary level set value represented by the following formula A: Equation A

Is the temporary level set value given to the i-th node of the lattice structure, m is the mass coefficient, V _j is the volume of the fluid particle j among the fluid particles, and W (x _ij , r _j ) is the fluid particle j Radial symmetric kernel function with radius equal to radius. The method according to claim 9 or 10, In the fluid particle forming step, the fluid particles are formed such that a drag force represented by Equation B and a lift force represented by Equation C act on the fluid particles. Fluid simulation method: Equation B

here,

Is the drag acting on the fluid particle, k _drag is the drag coefficient, r _i is the radius of the fluid particle,

Is the velocity of the fluid particle, and

Is the speed of the background fluid. Equation C

here, Is the _lift force acting on the fluid particles, k _lift is the lift coefficient, V _i is the volume of the fluid particles,

Is the velocity of the fluid particles,

Is the velocity of the background fluid, and ω _i is the vorticity

Calculated by The method according to claim 9 or 10, In the fluid particle forming step, the multi-phase fluid simulation method characterized in that for forming the fluid particles so that the vorticity confinement force represented by the following equation D to the fluid particles: [Equation D]

here,

Is the restraining force, ε is a preset proportional constant, ω is the vortex of the fluid particles, ρ _i is the density of fluid particles i, and

Is a generalized vortex position vector,

to be. The method according to claim 9 or 10, The fluid particles are agglomerated by the cohesive force represented by the following equation E to form a multi-phase fluid simulation method characterized in that to form the fluid particle population: [Equation E]

here,

Is the cohesion force acting between the fluid particle i and the fluid particle j, k _attraction is the proportional coefficient, W _attraction is a constant to easily determine the cohesion force by balancing the pressure between the fluid particles,

Uses the position vector between fluid particle i and fluid particle j

Where r _i and r _j are the radii of fluid particle i and j, and ρ _i is the density of fluid particle i, respectively. A computer-readable recording medium having recorded thereon a program for executing the multiphase fluid simulation method according to claim 9 or 10 on a computer.

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