CN117194859A

CN117194859A - Construction method and system of non-structural grid self-adaptive thin and efficient parallel high-precision algorithm framework based on intermittent Galerkin method

Info

Publication number: CN117194859A
Application number: CN202311065020.2A
Authority: CN
Inventors: 刘云龙; 孔琦; 曹远; 郝启航; 陈乐文; 熊骋望
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2023-08-23
Filing date: 2023-08-23
Publication date: 2023-12-08

Abstract

A construction method and a system of an unstructured grid self-adaptive thin and efficient parallel high-precision algorithm framework based on a discontinuous Galerkin method relate to the technical field of high-precision algorithm high-efficiency calculation. The method solves the problems that the existing intermittent Galerkin method has the characteristic of high precision, but the calculation efficiency is greatly reduced due to the large-scale increase of the calculation amount. The method comprises the following steps: determining grid subdivision and merging criteria; performing subdivision and merging operations; dynamically balancing CPU load; adjacent blocks information interactive communication and calculation; CPU communication and thread initialization, repeating the steps until obtaining the non-structural grid self-adaptive fine and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method. The invention is suitable for grid self-adaption and large-scale parallel technology of the intermittent Galerkin method.

Description

Construction method and system of non-structural grid self-adaptive thin and efficient parallel high-precision algorithm framework based on intermittent Galerkin method

Technical Field

The invention relates to the technical field of high-precision algorithm high-efficiency calculation.

Background

With the development of computer technology, simulation calculation of physical processes and phenomena in the fields of fluid and structural mechanics by a numerical simulation method has become a mainstream research means, and methods such as finite element, finite volume and the like are rapidly developed and applied. However, some more complex physical phenomena involving strong discontinuities, strong transients, etc. put higher demands on the accuracy of the numerical simulation algorithm, which cannot be satisfied by the conventional numerical methods, require the support of the high-accuracy algorithm. In the aspect of grid, the structured grid has high generation speed, simple data structure and high parallel computing efficiency, but has a narrow application range, is only suitable for regular boundary shapes, and the unstructured grid can process complex graphs, has good adaptability and low parallel computing efficiency.

The intermittent Galerkin method is a theoretical complete high-precision algorithm, is paid more attention to, removes the continuous restriction of unit basis functions on unit boundaries on the basis of the traditional finite element method, can easily realize high precision by selecting proper unit basis functions, namely self-adaptive p refinement, and is rapidly improved and developed. However, the high-precision characteristic of the numerical method also brings about large-scale increase of the calculated amount, greatly reduces the calculation efficiency, and limits the further expansion of the application field to a certain extent.

In the intermittent Galerkin method, each unit is only associated with adjacent units, the numerical format is compact, the method has great advantages in efficient parallel computing simulation, and meanwhile, the method has the processing capacity of unstructured grids, so that the efficient computing field of a high-precision algorithm becomes a research hot spot.

In summary, it becomes significant how to improve the calculation efficiency of high-precision algorithms such as intermittent galy.

Disclosure of Invention

The invention solves the problems that the calculation efficiency is greatly reduced due to the large-scale increase of the calculated amount although the existing intermittent Galerkin method has the characteristic of high precision.

In order to achieve the above object, the present invention provides the following solutions:

the invention adopts block-based AMR as a self-adaptive strategy, combines the advantages of structured and unstructured grids, and provides a method for constructing an unstructured grid self-adaptive refinement and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method, wherein grid self-adaptation is self-adaptive h refinement, and the method comprises the following steps:

s1, selecting an indicating variable according to the flow field characteristics, and formulating a self-adaptive criterion according to the indicating variable;

s2, searching a region of the concerned flow field characteristic detail according to the self-adaptive criterion, and marking an indication variable on the blocks at the corresponding position of the region to obtain the block subdivision level of each region;

S3, comparing the block subdivision grade of each region with the current grade to obtain subdivision or merging judgment conditions and grade difference conditions;

s4, carrying out subdivision or combination operation according to the subdivision or combination judgment conditions and the grade difference conditions to obtain a new subdivision or combination grid;

s5, resolving the numerical values on the original blocks grid to the new grid after subdivision or combination for L ₂ Projecting to obtain a projected block grid;

s6, sequencing the blocks grid of all areas in the flow field by using a Hillbert space filling curve to obtain a sequencing graph;

s7, splitting according to different region weights according to the ordering diagram, distributing splitting results to each computing core, and processing the information interaction layer grid of the projected blocks grid by adopting adjacent blocks data after each computing core is distributed to obtain the processed blocks grid;

s8, carrying out numerical calculation on the processed blocks grid by adopting a discontinuous Galao Jin Qiujie device;

and S9, communicating different CPU loads, initializing variables in threads, entering the next time increment step, and repeating the steps S2 to S8 until calculation is terminated to obtain an unstructured grid self-adaptive fine and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method.

Further, in a preferred embodiment, the marker indication variable in the step S2 is an indication variable for marking the subdivision of the grid.

Further, in a preferred embodiment, the marker indication variable in the step S2 may be a grid-merged indication variable.

Further, in a preferred embodiment, the subdivision in step S3 is determined under the condition that the level of the blocks subdivision in each area is greater than the current level.

Further, in a preferred embodiment, the combined determination in the step S3 is that the blocks subdivision level of each area is smaller than the current level.

Further, in a preferred embodiment, the level difference condition in the step S3 is that the level difference between adjacent blocks is not greater than 1.

Further, in a preferred embodiment, the processing in step S7 includes filling in assignment or defining boundary conditions.

The method for constructing the non-structural grid self-adaptive thin and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method can be realized by adopting computer software, so that the invention also provides a corresponding system for constructing the non-structural grid self-adaptive thin and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method, which comprises the following steps:

The storage device is used for selecting an indicating variable according to the flow field characteristics and formulating an adaptive criterion according to the indicating variable;

the storage device is used for searching a region of the detail of the flow field feature concerned according to the self-adaptive criterion, marking an indication variable on the blocks at the corresponding position of the region, and obtaining the subdivision level of the blocks of each region;

the storage device is used for comparing the block subdivision grade of each region with the current grade to obtain subdivision or combined judgment conditions and grade difference conditions;

the storage device is used for carrying out subdivision or combination operation according to the subdivision or combination judging condition and the grade difference condition to obtain a new subdivided or combined grid;

for solving values on the original blocks grid to L on the subdivided or merged new grid ₂ Projecting to obtain a storage device of a projected block grid;

the storage device is used for sequencing the blocks grid of all areas in the flow field by using a Hillbert space filling curve to obtain a sequencing graph;

the storage device is used for splitting according to different area weights according to the ordering diagram, distributing splitting results to each computing core, and processing the information interaction layer grid of the projected blocks grid by adopting adjacent blocks after each computing core is distributed to obtain the processed blocks grid;

A storage device for performing numerical computation on the processed blocks grid by using a discontinuous Galiao Jin Qiujie device;

the method is used for carrying out communication between different CPU loads, initializing variables in threads, entering the next time increment step, and repeating the steps until calculation is terminated, so as to obtain the storage device of the non-structural grid self-adaptive fine and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method.

The invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program executes the method for constructing the non-structural grid self-adaptive thin and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method when being run by a processor.

The invention also provides a computer device, which comprises a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method for constructing the non-structural grid self-adaptive thin and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method.

The beneficial effects of the invention are as follows:

1. the invention provides a construction method of an unstructured grid self-adaptive thin and efficient parallel high-precision algorithm framework based on a discontinuous Galerkin method, wherein the attached discontinuous Galerkin method adopts a universal framework of a conservation partial differential equation, and different problems can be solved conveniently by bringing in flux items and source items of interest. In addition, the algorithm framework adopts block-based AMR as a self-adaptive strategy, on one hand, an unstructured grid is adopted to define initial root blocks in the block layer, the algorithm framework has the advantage of processing complex graph boundaries, and on the other hand, the structured grid divided in the block layer has a simple data structure, so that the algorithm framework has higher calculation efficiency. And then, based on a block and quadtree structure, an algorithm framework of data communication between blocks with parent adjacent relations and between CPUs is established, the adaptive p and h refinement is flexibly carried out, meanwhile, the Hillbert space curve filling technology and SCF are adopted to dynamically balance the load between the CPUs, so that the balance of single CPU thread calculation tasks is achieved, the idle window waiting period of multi-core parallel calculation is reduced, the calculation task of the current time step is rapidly processed, and the calculation of the next time step is carried out. The method solves the problems that the existing intermittent Galerkin method has the characteristic of high precision, but the calculation efficiency is greatly reduced due to the large-scale increase of the calculation amount.

The invention is suitable for grid self-adaption and large-scale parallel technology of the intermittent Galerkin method.

Drawings

FIG. 1 is a flow chart of a method for constructing an unstructured grid adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method according to an embodiment I;

FIG. 2 is a block subdivision level quadtree structure internal relationship diagram according to one embodiment;

FIG. 3 is a graph of four types of interrelationships between adjacent blocks according to one embodiment;

FIG. 4 is a single block grid definition configuration diagram according to one embodiment;

FIG. 5 is a diagram of communication relationships between adjacent blocks according to one embodiment;

FIG. 6 is a schematic diagram of the recursive subdivision of the Hillbert curve in the first 3 subdivision levels in two-dimensional space according to one embodiment;

FIG. 7 is a Hillbert curve filling re-ordering arbitrary nodes in a two-dimensional space, with different colors of blocks representing partitions of different CPUs, as described in embodiment one;

FIG. 8 (a) is a square root block configuration diagram of an example of a linear transport equation test according to the eleventh embodiment;

FIG. 8 (b) is a diagram of a four root blocks configuration with relative rotation of shape distortions for a linear transport equation test example described in embodiment eleven;

FIG. 8 (c) is a diagram showing three root blocks configuration with relative rotation of shape distortion for a linear transport equation test example according to the eleventh embodiment;

FIG. 9 (a) is a graph of square root block values for an example linear transport equation test according to embodiment eleven;

FIG. 9 (b) is a graph of four root blocks values resulting from shape distortion with relative rotation for the linear transport equation test example described in embodiment eleven;

FIG. 9 (c) is a graph showing the results of three root blocks of relative rotation of shape distortions for the linear transport equation test example described in embodiment eleven;

wherein t=1.0;

FIG. 10 (a) is a density cloud plot with adaptive blocks distribution of the Euler equation Sedov point explosion problem described in embodiment eleven;

fig. 10 (b) is a graph of a y=0 section density numerical solution versus an exact solution of the euler equation Sedov point explosion problem according to the eleventh embodiment;

FIG. 11 is a schematic diagram of the dimensional parameters and flow fields of the Euler equation supersonic triangular prism and cylindrical bypass problem described in the eleventh embodiment;

FIG. 12 is a table of relative error between beta values of different adaptive subdivision levels and theoretical solutions for the supersonic triangular prism bypass flow problem of Euler equation according to the eleventh embodiment;

FIG. 13 (a) is a density gradient numerical schlieren plot of the Euler equation supersonic triangular prism bypass flow problem described in embodiment eleven;

FIG. 13 (b) is a density cloud plot with adaptive blocks distribution of the Euler equation supersonic triangular prism bypass flow problem described in embodiment eleven;

fig. 14 is a graph of a comparison of a numerical solution of a stagnation distance of a supersonic cylindrical bypass flow problem according to an eleventh embodiment of the present invention with a theoretical solution;

FIG. 15 (a) is a density gradient numerical schlieren plot of the Euler equation supersonic cylindrical bypass flow problem described in embodiment eleven;

FIG. 15 (b) is a density cloud plot with adaptive blocks distribution of the Euler equation supersonic cylindrical bypass flow problem described in embodiment eleven;

FIG. 16 (a) is a schematic diagram showing the problem of smoothing the trigonometric function of the Euler equation in the space P of the polynomial of the basis function according to the eleventh embodiment ¹ With adaptive blocks distribution;

wherein, the upper and lower subdivision level min/max=3/5;

FIG. 16 (b) is a schematic diagram showing the problem of smoothing the trigonometric function of the Euler equation in the space P of the polynomial of the basis function according to the eleventh embodiment ¹ Is provided with a density cloud picture with uniformly distributed blocks;

wherein, the upper and lower subdivision level min/max=5/5;

FIG. 17 (a) is a block diagram of 1 CPU with adaptive grid distribution for the Euler equation trigonometric function smoothing problem described in embodiment eleven;

FIG. 17 (b) is a plot of a partition of 2 CPUs with adaptive grid distribution for the Euler equation trigonometric function smoothing problem described in embodiment eleven;

FIG. 17 (c) is a partition diagram of 4 CPUs with adaptive grid distribution for the Euler equation trigonometric function smoothing problem described in embodiment eleven;

FIG. 17 (d) is a block diagram of 8 CPUs with adaptive grid distribution for the Euler equation trigonometric function smoothing problem described in embodiment eleven;

FIG. 17 (e) is a block diagram of 16 CPUs with adaptive grid distribution for the Euler equation trigonometric function smoothing problem described in embodiment eleven;

FIG. 17 (f) is a block diagram of 32 CPUs with adaptive grid distribution for the Euler equation trigonometric function smoothing problem described in embodiment eleven;

wherein, the upper and lower subdivision level min/max=3/5;

FIG. 18 (a) is a block diagram of a smooth problem of the trigonometric function of the Euler equation with 1 CPU distributed in a uniformly distributed grid according to the eleventh embodiment;

FIG. 18 (b) is a plot of the smooth problem of the trigonometric function of the Euler equation with 2 CPUs distributed in a uniformly distributed grid, according to the eleventh embodiment;

FIG. 18 (c) is a block diagram of the Euler equation trigonometric function smoothing problem with 4 CPUs of the uniformly distributed grid distribution described in embodiment eleven;

FIG. 18 (d) is a block diagram of the Euler equation trigonometric function smoothing problem with 8 CPUs of the uniformly distributed grid distribution described in embodiment eleven;

FIG. 18 (e) is a block diagram of the Euler equation trigonometric function smoothing problem described in embodiment eleven with 16 CPUs of uniform grid distribution;

FIG. 18 (f) is a block diagram of the Euler equation trigonometric function smoothing problem described in embodiment eleven with 32 CPUs distributed in a uniformly distributed grid;

wherein, the upper and lower subdivision level min/max=5/5;

FIG. 19 is a graph showing time-consuming curve changes of the trigonometric function smoothing problem of Euler equation according to the eleventh embodiment under the framework of adaptive and parallel algorithms with different numerical precision;

FIG. 20 is a table of error and numerical accuracy of the trigonometric function smoothing problem L1, L2 described in the eleventh embodiment;

fig. 21 is a table of time-consuming calculations for trigonometric function smoothing problem CPUs according to the eleventh embodiment.

Detailed Description

The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by those skilled in the art without departing from the spirit of the invention, which falls within the scope of the invention.

Referring to fig. 1 to 7, the present embodiment uses block-based AMR as an adaptive strategy, and combines the advantages of structured and unstructured grids to provide a method for constructing an unstructured grid adaptive refinement and efficient parallel high-precision algorithm framework based on the discontinuous galerkin method, wherein the grid adaptation is adaptive h refinement, and the method is as follows:

In practical application, as shown in fig. 1, the embodiment first determines the mesh score and the merging criterion: selecting proper indication variables according to the flow field characteristics to formulate a self-adaptive criterion for searching a region of the detail of the flow field characteristics concerned, and then marking grid subdivision or combined indication variables on blocks at corresponding positions to determine proper subdivision levels; the method comprises the following steps: the numerical calculation of the physical variables of the related flow field is realized by adopting a discontinuous Galerkin method, and the discontinuous Galerkin method considers the following conservation system in a two-dimensional space:

Where U, F, G and S are conservation vectors, flux vectors in the x and y directions and source term vectors, respectively. Considering a single cell Ω in the computational domain, the galy form of the above equation can be written as:

phi in _i Is a polynomial space P ^K One element in a complete set of basis functions, n= (n) _x ,n _y ) Is a unit edgeOutward unit normal, ++>And->Is the numerical flux. Representing a numerical solution as U _h ＝∑ _j＝i,N k _j φ _j The above equation can be written as a matrix form:

wherein M is a mass matrix,for the time derivative of the k matrix unknowns, R is the unified representation of the matrix on the right hand side.

Since the numerical flux is a single-valued function that depends on the solution on both sides of the interface, consistency, continuity and monotonicity conditions must be met. The Lax-Friedrichs flux was chosen here as follows:

where F may be F or G and α is the maximum eigenvalue of the system jacobian matrix.

Defining L (U) as an operator of PDE (Partial differential equation), the time stepping of the solution using the third-order longger-Kutta (range-Kutta) method in this embodiment can be expressed as:

U ⁽¹⁾ ＝U ⁽ⁿ⁾ +ΔtL(U ⁿ )

the intermittent Galerkin method is a universal framework of a conservation type partial differential equation, and different problems can be solved conveniently by bringing the flux item and the source item of interest.

Then performs subdivision and merging operations: comparing the subdivision level of the blocks of each region with the current level, determining whether subdivision or merging is required, and ensuring that the level difference between adjacent blocks after operation is not more than 1, wherein the level difference is based onPerforming subdivision merging operation on the basis, and solving values on the original blocks grid to a new grid for L ₂ And (5) projection. The method comprises the following steps: since the data structure of a block is a derivative of modern Fortran, it contains some scalar quantities representing the state of the block, data arrays storing intermediate variables and unknowns, and pointer links between other blocks. The pointer is associated with other blocks that are related to the current block, such as its parent block, child block, and neighboring blocks at the same subdivision level. A stack of interconnected blocks forms a quadtree structure, as shown in fig. 2. Root blocks (yellow blocks) have no parent blocks and the subdivision level is 1. First root blocks are created from user-given data and the adjacency between them is calculated from the topology. They may then be recursively subdivided to generate sub-blocks (blue blocks) at the next subdivision level. Thus, each root block will generate a quadtree structure. And calculating the adjacent relation of the new-born blocks according to the parent adjacent relation of the new-born blocks and the positions in the same level. The terminal end of the quadtree structure is defined as leaf blocks (green squares) which need to be solved for intermittent galkin.

To facilitate the processing of complex graph boundaries, the initial root blocks used to describe the computational domain may be defined by an unstructured grid, so that there is an arbitrary relative rotation between adjacent blocks, represented by array R. R is R _i The number of relative rotations of the i-th adjacent block with respect to the current block in the counterclockwise direction is shown in fig. 3. Thus, the sequence number of the neighbor block plane (edge) that is connected to the i-th plane (edge) of the current block can be calculated by the following formula, where P ₄ (x) =mod (x-1, 4) +1 is an operator used to map the working integers between 1 and 4.

I _f ＝P ₄ (i+2-R _i )；

Grid definition for individual blocks: each block is internally discretized intoThe node positions of the orthogonal units are given by block configuration node bilinear interpolation, and the obtained structured grid has a simple data structure, is beneficial to efficient calculation and uses N _seg =4 in N _seg =4 is for example, as shown in fig. 4. A layer of guard unit is defined at the block edge to realize communication between adjacent blocks, and the node position is calculated by bi-linear interpolation of block configuration nodes corresponding to the adjacent positions. In each time step of solving the intermittent Galerkin equation, only the actual units in the blocks are required to be solved, while the solution of the guard units is directly filled or assigned with boundary conditions from adjacent blocks, so that the correct boundary flux at the boundary is ensured.

Communication between adjacent blocks: communication between adjacent blocks is achieved by populating respective corresponding guard elements, in this embodiment a series of operators is defined as follows.

To rotate the operator, the solution is rotated N times counterclockwise; m is M _comb For a combination operator, combining the solutions of the 4 child units into a solution of the parent unit; />To split the operator, the solution for the nth child element is calculated by the given parent element.

The operator can be used for calculating an unknown solution of any unit, and similar to a block, the internal unit of the unknown solution also has a parent-child relationship. Fig. 5 is a filling process of 3 types of guard units, respectively, as follows:

(1) Filling with adjacent blocks of the same subdivision level. As in the communication between blocks a and B in fig. 5, the solution vector K of the target guard unit g is directly from the adjacent block corresponding unit g _n And performs the corresponding rotation operation:

(2) Filling with neighboring blocks of higher subdivision level. Communicating from block a to C as in fig. 5, the corresponding 4 subunits in adjacent blocks are grouped together to obtain a solution for the target guard unit:

(2) Filling with neighboring blocks of lower subdivision level. Communicating from block C to a as in fig. 5, obtaining a solution of the target guard unit by splitting the corresponding parent unit in the adjacent block:

Communication between inherited blocks: communication between inherited blocks is communication between parent and child blocks implemented in the subdivision and merging process. When one block needs to be subdivided, 4 sub-blocks are generated, the data of which passes L ₂ The projection inherits from the original parent block. In the reverse merge process, the parent block will inherit data from its 4 child blocks.

Dynamically balancing CPU load: sequencing all areas in a flow field through Hillbert space filling curves, splitting according to different area weights, and distributing the split areas to each computing core; the method comprises the following steps: the Hilbert space curve filling technology is adopted to dynamically balance the load among the CPUs and distribute the calculation tasks. The Hilbert space curve has a recursive nature of self-similarity and mapping between the coordinate sequences in the high-dimensional space and the one-dimensional space, as shown in fig. 6. The linear division of the sequence in one dimension ensures that the coordinates in the same partition in the high dimension space are close to each other. A square root block is first constructed containing all points and then subdivision operations are performed until there are at most 1 point in each leaf block. The points are then ordered by Hilbert space curve across all leaf blocks. By appropriate weight partitioning of the curve at each point, the partitioning is performed in a relationship where the same partition target blocks are adjacent to each other. The algorithm framework flexibly performs adaptive p and h refinement and adopts the SCF technology to dynamically balance loads, and the SCF technology can gradually change the partition with minimum data communication requirements when the grid is locally subdivided and merged. Fig. 7 demonstrates the process, where the green dots represent the dots to be ordered, and the lines connecting them represent the order.

CPU communication and thread initialization. The communication between different CPU loads is specifically as follows: an object is defined in the communication algorithm between CPUs. It comprises the following data structures:

an integer representing the target CPU process ID number with which communication is to be made;

a list of blocks and their required communication data ID numbers that should be packed and transmitted;

a list of blocks and their required communication data ID numbers that should be accepted and overwritten from the target CPU process;

two buffer arrays for holding data being transmitted and received.

Initializing variables in the thread, entering the next time increment step, and repeating the steps S2 to S8, wherein the steps are specifically as follows: initializing: initializing a parallel algorithm global constant; initializing root blocks according to the given data; the unknown number is initialized by iteration of given initial conditions, the segmentation and merging marks are calculated according to the self-adaptive criteria, and segmentation and load balancing are carried out in different CPU threads.

Solving a discontinuous Galerkin equation for a single time step: calculating critical time increments of all blocks according to CFL conditions; performing information interaction among threads to fill buffer blocks; dumping the solution to the temporary array; information interaction is carried out among the blocks so as to fill the guard unit; the intermittent Galerkin equation for each block is solved and the solution is updated.

The subdivision criterion is checked and the subdivision operation is performed again. Outputting the solution file to a local hard disk to obtain an unstructured grid self-adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method.

The implementation mode provides a construction method of an unstructured grid self-adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method, wherein the attached intermittent Galerkin method adopts a universal framework of a conservation partial differential equation, and different problems can be solved conveniently by bringing in flux items and source items of interest. In addition, the algorithm framework adopts block-based AMR as a self-adaptive strategy, on one hand, an unstructured grid is adopted to define initial root blocks in the block layer, the algorithm framework has the advantage of processing complex graph boundaries, and on the other hand, the structured grid divided in the block layer has a simple data structure, so that the algorithm framework has higher calculation efficiency. And then, based on a block and quadtree structure, an algorithm framework of data communication between blocks with parent adjacent relations and between CPUs is established, the adaptive p and h refinement is flexibly carried out, meanwhile, the Hillbert space curve filling technology and SCF are adopted to dynamically balance the load between the CPUs, so that the balance of single CPU thread calculation tasks is achieved, the idle window waiting period of multi-core parallel calculation is reduced, the calculation task of the current time step is rapidly processed, and the calculation of the next time step is carried out. The method solves the problems that the existing intermittent Galerkin method has the characteristic of high precision, but the calculation efficiency is greatly reduced due to the large-scale increase of the calculation amount.

In the second embodiment, the marking indicating variable of the step S2 in the method for constructing the non-structural grid adaptive subdivision and efficient parallel high-precision algorithm framework based on the discontinuous galerkin method according to the first embodiment is exemplified, and the marking indicating variable is an indicating variable for marking grid subdivision.

In the third embodiment, the method for constructing the non-structural grid adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent galerkin method according to the first embodiment is exemplified by the marker indication variable in the step S2, and the marker indication variable may also be a grid merging indication variable.

In the fourth embodiment, the judging condition of subdivision in step S3 in the method for constructing the non-structural grid adaptive subdivision and efficient parallel high-precision algorithm framework based on the discontinuous gallog method according to the first embodiment is exemplified, and the subdivision level of blocks in each region is greater than the current level.

In the fifth embodiment, the merging judgment condition in the step S3 in the method for constructing the non-structural grid adaptive subdivision and efficient parallel high-precision algorithm framework based on the discontinuous gallog method according to the first embodiment is exemplified, and the blocks subdivision level of each region is smaller than the current level.

In the sixth embodiment, the level difference condition of step S3 in the method for constructing the non-structural grid adaptive thin and efficient parallel high-precision algorithm framework based on the discontinuous gallog method according to the first embodiment is exemplified, where the level difference condition is that the level difference between adjacent blocks is not greater than 1.

In the seventh embodiment, the process of step S7 in the method for constructing the non-structural grid adaptive refinement and efficient parallel high-precision algorithm framework based on the discontinuous galerkin method according to the first embodiment is exemplified, where the process includes filling assignment or defining a boundary condition.

The eighth embodiment provides a system for constructing an unstructured grid self-adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method, wherein the system is as follows:

The present embodiment provides a computer-readable storage medium having a computer program stored thereon, which when executed by a processor, performs the method for constructing an unstructured grid adaptive refinement and efficient parallel high-precision algorithm framework according to any one of the first to seventh embodiments.

The tenth embodiment provides a computer device, which includes a memory and a processor, where the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method for constructing the non-structural grid adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent galkin method according to any one of the first to seventh embodiments.

An eleventh embodiment is described with reference to fig. 8 to 21, in which any one of the first to seventh embodiments is a verification description of an unstructured grid adaptive refinement and efficient parallel high-precision algorithm framework based on the intermittent galerkin method:

and (3) verifying by adopting a linear transport equation, wherein the linear transport equation is as follows:

Wherein the initial condition is u (x, y, 0) = [ cos (2πx) -1][cos(2πy)-1]The computational domain is selected as [0,1]×[0,1]The outside is a periodic boundary condition. Three sets of root blocks are used to test the performance of the adaptive algorithm framework. The first set is a square root block covering the entire computational domain, the second and third sets are root blocks containing 4 and 3 shape distortions, respectively, with relative rotations, as shown in fig. 8. The average value of u in the intermittent galy unit is selected to set the upper and lower limit parameters of the adaptive subdivision criterion to 3.0 and 1.0 respectively, and the minimum and maximum subdivision levels are set to 3 and 5 respectively (which can be expressed as min/max=3/5). Fig. 9 shows the numerical calculation result at t=1.0, and the black line represents the cell boundary. The result is better matched with the accurate solution, L ₂ Error of 2.2e respectively ^-8 、2.7e ^-8 And 6.4e ^-8 Indicating that the algorithm framework is able to handle inconsistent grids without loss of accuracy.

The algorithm precision and the algorithm efficiency of the parallel algorithm framework are further verified by adopting Euler problem calculation examples corresponding to Euler equations, and the Euler two-dimensional system is considered as follows:

where ρ, u, v are the density and velocity components in the x, y directions, respectively, p is the fluid pressure,e is the energy content per unit mass for the total energy. In order to block the Euler equation set, an ideal gas state equation is introduced as follows, wherein gamma is an adiabatic index, and is taken as 1.4.

p＝ρe(γ-1)；

The two-dimensional sedove point explosion problem is a typical strong impact low density euler algorithm, and initial conditions are set:

where Δx and Δy are the grid dimensions in two directions, and the calculated domain is [ -1.1,1.1]×[-1.1,1.1]Defined by a square root block, the outside is the outflow boundary condition. Setting N _seg The minimum and maximum subdivision levels are set to 4 and 6 (min/max=4/6), respectively, i.e. the minimum of the computational domain grid is 1.1/40 and the maximum is 1.1/160. The upper and lower limit parameters of the density average value setting subdivision criterion are respectively 1.2 and 1.01, and the calculation time is t=1.0.

Among them, the Sedov point explosion problem related results are shown in fig. 10. The density value solution of the profile is well matched with the accurate solution, and the distribution of the self-adaptive blocks also proves that the subdivision region can well track the explosion crest value region and can better approach the accurate solution.

Therefore, the unstructured grid self-adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method has good adaptability to the problem of strong intermittent impact, and the self-adaptive area has good tracking and capturing capacity to the concerned area.

The precision of the algorithm framework and the adaptive grid subdivision are further verified by using the supersonic bypass flow problem:

firstly, considering the supersonic motion condition of the triangular prism, the size and flow field schematic diagram of the supersonic flow field are shown in fig. 11, the supersonic flow field finally forms an attached oblique shock wave at the vertex of the triangular prism, the angle between the attached oblique shock wave and the triangular axis is beta, and the angle between the attached oblique shock wave and the incoming flow Mach number Ma and the triangular prism half-vertex angle theta meet the following formula:

The triangular prism two-dimensional plane dimension parameter takes h=0.5, θ=20°, and the vertex coordinates are (0.5, 1.0). The calculation domain is [0,2]×[0,2]To the left is an inflow boundary, which is the same as the initial condition of the computational domainOutflow boundary conditions are used on the right and upper and lower sides. Numerical calculation is carried out on the scene by adopting a discontinuous Galay Jin Qiujie device, mach number Ma=2 is selected, and the AM is defined by adopting speed divergence and rotationR self-adaptive criterion, tracking details of flow fields such as shock wave, vortex and the like, and setting N _seg And 4, respectively taking the self-adaptive upper and lower subdivision grades of min/max=1/2, 1/3,1/4 and 1/5 to perform numerical calculation, stopping calculation after the shock wave structure is stable, and obtaining a theoretical value of the working condition beta of 53.46 degrees according to the formula, thereby obtaining a relative error table of the numerical value and the theoretical solution of different self-adaptive subdivision grades beta, as shown in fig. 12. The intermittent Galerkin method with an adaptive algorithm framework is shown to have extremely high accuracy for the basic morphological simulation of shock waves.

Fig. 13 is a numerical result of an adaptive subdivision level of min/max=1/5. The density numerical schlieren graph shows that the triangular prism head has clear and sharp attached oblique shock wave structure, and there is great density gradient at two corners of the rigid body tail, and the generated two shock waves move inwards to finally meet at the rigid body flow wake, and the shock waves and the vortex structure interact to form a funnel-shaped complex flow field area and swing up and down. The AMR self-adaptive blocks distribution diagram shows that the encryption area of the flow field has good following capability on the detail area of the shock wave and triangular prism tail flow field, so that more calculation resources can be distributed in the area concerned by people, and the calculation economy and efficiency are improved.

For the problem of supersonic velocity bypass of the cylinder, bow-shaped shock wave is generated at the head of the cylinder, as shown in fig. 11, a theoretical solution exists for the stagnation distance delta between the cylinder and the upstream stagnation point of the cylinder, wherein R is the radius of the cylinder:

taking the radius of the cylinder as R=0.2 and the center coordinates (0.0 ). The calculation domain is [ -1.0,2.6]×[-1.8,1.8]The left is the inflow boundary, which is (ρ, u, v, p) = (1.4, ma,0, 1) as the computational domain initial condition, and the right and upper and lower are outflow boundary conditions. AMR self-adaptive criterion is consistent with the supersonic bypass of the triangular prism, and N is set _seg =4, the adaptive up-down subdivision level is taken as min/max=1/5, the Mach numbers are respectively selected as ma= 1.5,1.7,2.0,2.5,3.0,3.5,4.0, and the counting is stopped after the shock wave structure is stableThe numerical results of the intermittent galy adaptive algorithm, such as shown in fig. 14, are well matched with the theoretical values, which indicates that the characteristic structural variables of the shock wave in the embodiment have good simulation accuracy.

FIG. 15 is a graph of the above-described numerical schlieren of density of the cylindrical supersonic bypass flow field and AMR adaptive blocks. The clear bow-shaped split shock wave structure in front of the cylindrical incoming flow can be seen, a funnel-shaped structure similar to a triangle rigid body is generated at the tail part of the cylindrical incoming flow, the split shock waves are interacted and separated through the intersection, an obvious flowing-around vortex structure is generated, and the cylindrical incoming flow gradually swings upwards and downwards to fall off to form a complex flow field structure. The self-adaptive encryption area can be well attached to the flow field structures such as bow-shaped disjunctor shock waves, separation shock waves, orbiting vortex and the like.

The verification result shows that the intermittent Galerkin method with the AMR self-adaptive subdivision framework has good precision on simulation of main flow field characteristic structures such as basic form of shock waves when the supersonic speed problem is processed, the self-adaptive local encryption area accurately captures and tracks the details of the flow field, the area needing high resolution is focused, and the self-adaptive algorithm framework of the embodiment is effectively verified.

The above-mentioned calculation example verifies the effectiveness of AMR self-adaptive algorithm framework of algorithm, the encryption area can track the flow field detail according to the problem demand, has reduced the grid calculated amount on the calculation scale, will follow the smooth problem of trigonometric function of Euler equation, carry on the quantitative comparison to precision and computational efficiency of AMR self-adaptive and parallel algorithm, check the effectiveness and universality of the high-accuracy algorithm.

The calculation domain is [0,2] × [0,2], the initial time is defined by four 1×1 square root blocks, the four sides are defined as periodic boundary conditions, and the initial conditions are as follows: ρ (x, y, 0) =1+0.2sin [ pi (x+y) ], u (x, y, 0) =0.7, v (x, y, 0) =0.3, p (x, y, 0) =1. The density is exactly solved as ρ (x, y, t) =1+0.2sin [ pi (x+y-t) ], and the calculation time is t=2.0.

Firstly, setting all root blocks to have the same AMR adaptive level, respectively taking the adaptive up-and-down level as min/max=1/1, 2/2,3/3,4/4,5/5,i.e. using a uniform grid inspection algorithm, summarizing to obtain L ₁ 、L ₂ The error and numerical precision order are shown in fig. 20. Three basis function polynomials space P ¹ ，P ² ，P ³ The respective required numerical accuracy requirements are achieved, and the algorithm framework can maintain the required numerical accuracy requirements according to specific situations, similar to the previous calculation example.

In order to check the effectiveness of AMR self-adaption and MPI parallel algorithm frameworks in the algorithm, the AMR self-adaption upper and lower grades of min/max=3/5 and 5/5 are respectively taken, namely, the computing domains with self-adaption subdivision grids and uniformly distributed grids are respectively arranged, wherein the condition of min/max=3/5 selects the density average value to set the upper and lower limit parameters of the subdivision criterion to be 1.0. FIG. 16 is a space P using a basis function polynomial ¹ For the former encryption region, the self-adaptive and uniform grid calculation results are mainly distributed in the region with the density larger than 1.0. And (4) calculating the working conditions by adopting AMR and MPI parallel algorithm frameworks and respectively taking CPU numbers of 1,2,4,8,16 and 32, and collecting to obtain CPU calculation time-consuming data as shown in figure 21.

As can be seen from fig. 21, the AMR adaptive algorithm can effectively reduce the blocks and the number of units according to the flow field data, and basically reduce the calculation amount, and the calculation amount reduction ratio and the time consumption reduction ratio are approximately equivalent from the point of calculating time consumption of different CPU numbers. In MPI parallel aspect, hillbert space curve is adopted to fill load among dynamically balanced CPUs, the number of blocks of the adaptive grid and the uniformly distributed grid is far more than the number of the CPUs, so that each CPU resource can be reasonably utilized in parallel operation, FIG. 17 is a CPU partition diagram of an adaptive grid computing domain, different colors represent different CPU partitions, a parallel algorithm can divide computing tasks to each CPU thread as evenly as possible, so that the time consumption of each CPU is as same as possible, the idle window waiting period of multi-core parallel computing is reduced, the computing tasks of the current time step are rapidly processed and the computing tasks of the next time step are carried out, the computing domain has 3 subdivision levels, the computing task partition is regular when the number of the CPUs is 1,2 and 4, the CPU resource is limited by the different computing domain grid sizes, a partition structure with small color partition is started, the general subdivision level is high, the grids are small and dense, the subdivision level of the partitions is low, the grids are large, but the computing tasks of different partitions are basically equivalent, and the computing tasks of different partitions can be calculated with high efficiency. For the uniform grid, as shown in fig. 18, the calculation tasks can be completely averaged to each CPU, and the partition is more regular. Three time-consuming curve changes of numerical precision under the frames of AMR adaptive and MPI parallel algorithms can be plotted according to the data of FIG. 21, as in FIG. 19. According to the self-adaptive criterion, the subdivision encryption grids only need to be distributed in the flow field area needing to be concerned, the self-adaptive algorithm can reduce the calculation time consumption by reducing the grid calculation amount, the parallel algorithm mainly dynamically balances the load among the CPUs, the calculation tasks are distributed for multi-threading and are calculated together, and the calculation time consumption is reduced approximately correspondingly along with the increase of the number of the CPUs, so that the calculation efficiency is greatly improved.

In summary, the method for constructing the non-structural grid adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent galliaojin method according to the embodiment adopts a universal framework of a conservation partial differential equation, and can conveniently solve different problems by bringing in flux items and source items of interest. In addition, the algorithm framework adopts block-based AMR as a self-adaptive strategy, on one hand, an unstructured grid is adopted to define initial root blocks in the block layer, the algorithm framework has the advantage of processing complex graph boundaries, and on the other hand, the structured grid divided in the block layer has a simple data structure, so that the algorithm framework has higher calculation efficiency. And then, based on a block and quadtree structure, an algorithm framework of data communication between blocks with parent adjacent relations and between CPUs is established, the adaptive p and h refinement is flexibly carried out, meanwhile, the Hillbert space curve filling technology and SCF are adopted to dynamically balance the load between the CPUs, so that the balance of single CPU thread calculation tasks is achieved, the idle window waiting period of multi-core parallel calculation is reduced, the calculation task of the current time step is rapidly processed, and the calculation of the next time step is carried out. The method solves the problems that the existing intermittent Galerkin method has the characteristic of high precision, but the calculation efficiency is greatly reduced due to the large-scale increase of the calculation amount.

Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.

In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.

The above description is only an example of the present invention and is not limited to the present invention, but various modifications and changes will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. The method for constructing the non-structural grid self-adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method is characterized by comprising the following steps of:

2. The method for constructing an unstructured grid adaptive subdivision and efficient parallel high-precision algorithm framework based on the intermittent galerkin method according to claim 1, wherein the marker indication variable in the step S2 is an indication variable of the marker grid subdivision.

3. The method for constructing an unstructured grid adaptive refinement and efficient parallel high-precision algorithm framework based on the intermittent galerkin method according to claim 1, wherein the marker indication variable in the step S2 may be a grid-merged indication variable.

4. The method for constructing an unstructured grid adaptive subdivision and efficient parallel high-precision algorithm framework based on the intermittent gallog method according to claim 1, wherein the subdivision judging condition in the step S3 is that the blocks subdivision level of each area is larger than the current level.

5. The method for constructing an unstructured grid adaptive subdivision and efficient parallel high-precision algorithm framework based on the intermittent gallog method according to claim 1, wherein the merging judgment condition in the step S3 is that the blocks subdivision level of each region is smaller than the current level.

6. The method for constructing an unstructured grid adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent gallog method according to claim 1, wherein the level difference condition in the step S3 is that the level difference between adjacent blocks is not greater than 1.

7. The method for constructing an unstructured grid adaptive refinement and efficient parallel high-precision algorithm framework based on the intermittent galerkin method according to claim 1, wherein the processing in step S7 includes filling assignment or defining boundary conditions.

8. The construction system of the non-structural grid self-adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent Galerkin method is characterized in that the system is as follows:

9. A computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the method for constructing the non-structural grid adaptive thin and efficient parallel high-precision algorithm framework based on the intermittent galerkin method according to any one of claims 1 to 7 is executed.

10. A computer device, characterized by: the device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the construction method of the unstructured grid self-adaptive thin and high-efficiency parallel high-precision algorithm framework based on the intermittent Galerkin method according to any one of claims 1 to 7.