CN106934185B - A Fluid-Structure Interaction Multiscale Flow Simulation Method for Elastic Media - Google Patents

Abstract

The invention discloses a kind of multiple dimensioned flow simulating methods of the fluid structurecoupling of elastic fluid.This method comprises: obtaining reservoir geology parameter and mechanics parameter, oil reservoir geometrical model is established, and multiple dimensioned grid dividing is carried out to oil reservoir geometrical model, obtain multiple dimensioned grid system；Based on multiple dimensioned grid system, establish mass-conservation equation and momentum conservation equation, realize the real simulation of changeability medium seepage flow situation, local momentum conservation equation is solved using multi-scale finite element method, obtain multiple dimensioned displacement basic functions, using multi-scale Simulation finite difference method Part mass conservation equation, multiple dimensioned speed basic function and multiple dimensioned pressure basic function are obtained, to guarantee the conservativeness calculated and accuracy；The flow simulating on large scale coarse grid is realized by multiple dimensioned basic function, and according to the mapping relations between large scale solution and small scale solution, the small scale solution of refined net unit is obtained, to reduce calculation amount.

Description

A Fluid-Structure Interaction Multiscale Flow Simulation Method for Elastic Media

technical field

The invention relates to the field of porous medium fluid-solid coupling flow simulation, in particular to a fluid-solid coupling multi-scale flow simulation method of elastic medium.

Background technique

The underground medium has strong stress sensitivity, and the stress in the reservoir has a significant impact on productivity prediction, uncertainty analysis and risk assessment, etc., and the influence of stress should be fully considered in reservoir numerical simulation. However, in actual reservoir applications, due to the multi-scale nature of reservoir geology and geometric properties, as well as the large spatial scale of the reservoir, the simulation time scale is long, so the traditional numerical method firstly divides the area into fine grids, and then finely The amount of simulation calculations on the scale is huge, which exceeds the existing computing power. In recent years, with the development of multi-scale methods, experts and scholars at home and abroad have begun to apply multi-scale methods to nonlinear flow simulation of heterogeneous reservoirs. The multi-scale method builds a large-scale equation system by locally calculating the multi-scale basis functions. After obtaining the large-scale solution, the multi-scale method can obtain a small-scale fine solution with high accuracy based on the multi-scale basis function mapping. The multi-scale method has a scale The calculation speed of the upgraded method has high calculation accuracy. However, the development of multi-scale now mainly focuses on multiphase flow simulation, especially the solution of elliptic pressure equation, which rarely involves the factors of mechanical deformation of the medium, and currently only The multi-scale Galerkin finite element method is used to solve fluid-solid coupling problems, but the multi-scale finite element method is based on the Galerkin finite element framework, so the local conservation of velocity cannot be guaranteed in the construction of multi-scale velocity basis functions. Not suitable for multiphase flow calculations.

Therefore, it is imperative to find a new numerical method that can reduce the calculation amount and ensure the calculation accuracy.

Contents of the invention

The object of the present invention is, in order to overcome the technical defects of the existing fluid-solid coupling reservoir flow simulation method, to obtain a fluid-solid coupling flow simulation method that can reduce the amount of calculation and has higher calculation accuracy, and provides a Fluid-structure coupling multiscale flow simulation method for elastic media.

To achieve the above object, the present invention provides the following scheme:

A fluid-solid coupling multi-scale flow simulation method for elastic media, comprising the following steps:

Obtain geological parameters and mechanical parameters of the reservoir, and establish a geometric model of the reservoir;

Perform multi-scale grid division on the reservoir geometry model to obtain a multi-scale grid system including coarse grid subsystem and fine grid subsystem;

Based on the multi-scale grid system, the local flow area is selected, the local mass conservation equation of the flow area is established, and the multi-scale finite element method is used to solve the local momentum conservation equation to obtain the multi-scale displacement basis function;

Based on the multi-scale grid system, the flow area is selected, the local momentum conservation equation of the flow area is established, and the multi-scale simulation finite difference method is used to solve the local mass conservation equation to obtain the multi-scale velocity basis function and the multi-scale pressure basis function;

Based on the multi-scale principle and multi-scale displacement basis function, multi-scale velocity basis function and multi-scale pressure basis function, the macro-large-scale solution of the coarse grid unit is obtained, and the mapping relationship between the macro-large-scale solution and the small-scale solution is obtained;

According to the macroscopic large-scale solution and the mapping relationship between the large-scale solution and the small-scale solution, the small-scale solution of the fine grid unit is obtained.

Optionally, the specific steps of the multi-scale grid division include:

According to the size of the research area, determine the large-scale coarse grid step size and quantity in each spatial direction, and use the orthogonal grid to divide the reservoir geometric model into a small-scale fine grid to obtain a fine grid subsystem;

On the basis of the small-scale fine grid, a load balancing algorithm is used to construct a coarse grid subsystem, and the coarse grid units in the coarse grid subsystem are formed by interconnecting the fine grid units in the fine grid subsystem;

A multi-scale grid system is composed of the coarse grid subsystem and the fine grid subsystem.

Optionally, the fine grid subsystem includes basic characteristic parameters and mechanical parameters of reservoir rocks and fluids.

Optionally, the specific steps of obtaining the multi-scale displacement basis function include:

Considering each coarse grid unit as a local flow region Ω, the momentum conservation equation of the local flow region is established:

Among them, C _dr is the elastic tensor, l is the time interval l=[0,t], u and p represent the displacement vector and pressure respectively, I is the identity matrix, b is the Biot coefficient, is a symmetric gradient operator;

Select the boundary condition φ ⁱ (x _j ) = δ _ij , δ _ij is the Kronecker symbol, use the multi-scale finite element method to solve the local momentum conservation equation, and obtain the multi-scale displacement basis function of each coarse grid unit And construct the multi-scale displacement basis function matrix in is a small-scale displacement basis function, and the small-scale displacement basis function is the basis function selected by the displacement variable when performing small-scale fine grid calculations, is the discrete value of displacement on the ith fine grid node in the coarse grid unit, is the number of fine grid unit nodes in the coarse grid unit.

Optionally, the specific step of obtaining the multi-scale velocity basis function and the multi-scale pressure basis function includes: treating two adjacent coarse grid cells as a flow region Ω' to ensure local conservation, and establishing the The local mass conservation equation for the flow region:

Among them, b is the Biot coefficient, l is the time interval l=[0,t], M _b is the Biot modulus, is the derivative of displacement with respect to time, is the derivative of pressure with respect to time, and λ is the fluid flow coefficient.

Select closed boundary conditions, use the multi-scale simulation finite difference method to solve the local mass conservation equation, and obtain the multi-scale pressure basis function corresponding to each coarse grid cell Multiscale velocity basis functions corresponding to each coarse grid boundary And construct the multiscale pressure basis function matrix and the multiscale velocity basis function matrix in, and are the small-scale pressure basis function and the small-scale velocity basis function respectively, the small-scale pressure basis function is the basis function of the pressure variable when the small-scale fine grid calculation is performed, and the small-scale velocity basis function is the small-scale velocity basis function In fine grid calculation, the basis function of the velocity variable, is the discrete value of pressure on the boundary of the ith fine grid in the coarse grid unit, is the velocity discrete value on the boundary of the ith fine grid in the coarse grid unit, is the number of fine grid units in the coarse grid unit; is the number of boundaries of the fine grid unit in the coarse grid unit.

Optionally, the specific steps of obtaining the macroscopic large-scale solution of the coarse grid unit include:

The multi-scale displacement basis function matrix, the multi-scale pressure basis function matrix and the multi-scale velocity basis function matrix are assembled into a mapping operator Φ,

which is

Construct the large-scale stiffness matrix A=ΦA ^f Φ ^T , where A ^f is the small-scale stiffness matrix, and the small-scale stiffness matrix is the stiffness matrix formed after discretizing the momentum conservation equation and the momentum conservation equation on the small-scale fine grid , the specific elements include the mechanical stiffness matrix, the simulation finite difference coefficient matrix, and the compression term coefficient matrix. On this basis, a large-scale equation system Ax=b is formed, where b is the right-hand term of the equation system, including source-sink items, and displacement boundary conditions and stress boundary conditions;

Solve the coupled large-scale equations to obtain the macroscopic large-scale solution of the coarse grid unit, including large-scale displacement u ^c , large-scale pressure p ^c , and large-scale velocity v ^c .

Optionally, the specific steps of obtaining the small-scale solution of the fine grid unit include:

Construct mapping matrices N _u , N _p , N _v , where Nu _is a matrix with all multiscale displacement basis functions as column vectors, N _p is a matrix with all multiscale pressure basis functions as column vectors, and N _v is a matrix with all multiscale velocity basis functions as a matrix of column vectors;

According to the mapping matrix, the corresponding relationship between the macroscopic large-scale solution and the small-scale solution is: u ^f =N _u u ^c , p ^f ≈Ip ^c +N _p D _λ v ^c , v ^f =N _v v ^c , combined with the macroscopic large-scale solution of the coarse grid unit, the small-scale solution of the fine grid unit is obtained, where u ^f , p ^f , and v ^f represent the small-scale displacement, small-scale pressure and small-scale velocity respectively, and I is the identity matrix, and D _λ is the fluidity coefficient matrix.

According to the specific embodiments provided by the invention, the invention discloses the following technical effects:

The invention discloses a fluid-solid coupled multi-scale flow simulation method for elastic media, using mass conservation equations and momentum conservation equations to realize the real simulation of seepage in variable media, and using multi-scale finite element methods to solve local momentum conservation equations to obtain multi-scale displacements Basis functions, using the multi-scale simulation finite difference method to solve the local mass conservation equations to obtain multi-scale velocity basis functions and multi-scale pressure basis functions, construct large-scale fluid-solid coupling equations through multi-scale basis functions and obtain large-scale coarse grid solutions, including Large-scale displacement solution, pressure solution and velocity solution; according to the mapping relationship between the large-scale solution and the small-scale solution, the small-scale solution of the fine grid unit is obtained, which greatly reduces the amount of calculation while ensuring the accuracy of fluid-solid coupling flow simulation , can more comprehensively simulate oilfield development dynamics, and provide technical support for efficient development of oil reservoirs.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some of the present invention. Embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without paying creative labor.

Fig. 1 is a flow chart of an embodiment of a fluid-structure coupling multi-scale flow simulation method for elastic media provided by the present invention.

Fig. 2 is a schematic diagram of a multi-scale grid system of a fluid-solid coupling multi-scale flow simulation method for elastic media provided by the present invention.

Fig. 3 is a schematic diagram of obtaining multi-scale displacement basis functions of a fluid-solid coupling multi-scale flow simulation method for elastic media provided by the present invention.

Fig. 4 is a flowchart of another embodiment of a fluid-structure coupling multi-scale flow simulation method for elastic media provided by the present invention.

Detailed ways

The purpose of the present invention is to provide a fluid-solid coupling multi-scale flow simulation method for elastic media.

In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Fig. 1 is a flowchart of an embodiment of a fluid-solid coupling multi-scale flow simulation method of elastic media provided by the present invention. As shown in Fig. 1, as a possible implementation mode, a fluid-solid coupling multi-scale The scale flow simulation method includes the following steps:

S1 Obtain the geological parameters and mechanical parameters of the reservoir, and establish the geometric model of the reservoir;

S2 performs multi-scale grid division on the geometric model of the reservoir, and obtains a multi-scale grid system including a coarse grid subsystem and a fine grid subsystem;

S3 is based on the multi-scale grid system, selects the local flow area, establishes the local mass conservation equation of the flow area, and uses the multi-scale finite element method to solve the local momentum conservation equation to obtain the multi-scale displacement basis function;

S4 is based on the multi-scale grid system, selects the flow area, establishes the local momentum conservation equation of the flow area, and solves the local mass conservation equation by using the multi-scale simulation finite difference method to obtain the multi-scale velocity basis function and the multi-scale pressure basis function;

S5 is based on the multi-scale principle and multi-scale displacement basis function, multi-scale velocity basis function and multi-scale pressure basis function to obtain the macro-large-scale solution of the coarse grid unit, and obtain the mapping relationship between the macro-large-scale solution and the small-scale solution ;

S6 Obtain the small-scale solution of the fine grid unit according to the macroscopic large-scale solution and the mapping relationship between the large-scale solution and the small-scale solution.

The specific steps of multi-scale grid division described in step S2 include:

According to the size of the research area, determine the large-scale coarse grid step size and quantity in each spatial direction, and use the orthogonal grid to divide the reservoir geometric model into a small-scale fine grid to obtain a fine grid subsystem;

On the basis of the small-scale fine grid, a load balancing algorithm is used to construct a coarse grid subsystem, and the coarse grid units in the coarse grid subsystem are formed by interconnecting the fine grid units in the fine grid subsystem;

A multi-scale grid system is composed of the coarse grid subsystem and the fine grid subsystem, and the multi-scale grid system is shown in FIG. 2 .

The coarse grid subsystem includes basic properties of rock and fluid, and the fine grid subsystem includes reservoir parameters and mechanical parameters.

The specific steps of obtaining the multi-scale displacement basis function described in step S3 include:

As shown in Figure 3, each coarse grid unit is regarded as a local flow region Ω, and the momentum conservation equation of the local flow region is established:

Among them, C _dr is the elastic tensor, l is the time interval l=[0,t], u and p represent the displacement vector and pressure respectively, I is the identity matrix, b is the Biot coefficient, is a symmetric gradient operator, preferably, Ω=Ω _i , where Ω _i represents the area of the ith coarse grid unit in the multi-scale grid system;

Select the boundary condition φ ⁱ (x _j ) = δ _ij , δ _ij is the Kronecker symbol, use the multi-scale finite element method to solve the local momentum conservation equation, and obtain the multi-scale displacement basis function of each coarse grid unit And construct the multi-scale displacement basis function matrix in is a small-scale displacement basis function, and the small-scale displacement basis function is the basis function selected by the displacement variable when performing small-scale fine grid calculations, is the discrete value of displacement on the ith fine grid node in the coarse grid unit, is the number of fine grid unit nodes in the coarse grid unit.

The specific steps for obtaining the multi-scale velocity basis function and the multi-scale pressure basis function described in step S4 include:

Two adjacent coarse grid cells are regarded as a flow region Ω' to ensure local conservation, and the local mass conservation equation of the flow region is established:

Among them, b is the Biot coefficient, l is the time interval l=[0,t], M _b is the Biot modulus, is the derivative of displacement with respect to time, is the derivative of pressure to time, λ is the fluid flow coefficient, preferably, Ω'=Ω _i +Ω _j , Ω _j represents the jth coarse grid adjacent to the i-th coarse grid unit in the multi-scale grid system area of the unit;

Select closed boundary conditions, use the multi-scale simulation finite difference method to solve the local mass conservation equation, and obtain the multi-scale pressure basis function corresponding to each coarse grid cell Multiscale velocity basis functions corresponding to each coarse grid boundary And construct the multiscale pressure basis function matrix and the multiscale velocity basis function matrix in, and are the small-scale pressure basis function and the small-scale velocity basis function respectively, the small-scale pressure basis function is the basis function of the pressure variable when the small-scale fine grid calculation is performed, and the small-scale velocity basis function is the small-scale velocity basis function In fine grid calculation, the basis function of the velocity variable, is the discrete value of pressure on the boundary of the ith fine grid in the coarse grid unit, is the velocity discrete value on the boundary of the ith fine grid in the coarse grid unit, is the number of fine grid units in the coarse grid unit; is the number of boundaries of the fine grid unit in the coarse grid unit.

The specific steps of obtaining the macroscopic large-scale solution of the coarse grid unit described in step S5 include:

The multi-scale displacement basis function matrix, the multi-scale pressure basis function matrix and the multi-scale velocity basis function matrix are assembled into a mapping operator Φ,

which is

Construct the large-scale stiffness matrix A=ΦA ^f Φ ^T , where A ^f is the small-scale stiffness matrix, and the small-scale stiffness matrix is the stiffness matrix formed after discretizing the conservation of momentum equation and the conservation of momentum equation on the fine grid, specifically The elements include the mechanical stiffness matrix, the simulation finite difference coefficient matrix, and the compression term coefficient matrix. On this basis, a large-scale equation system Ax=b is formed, where b is the right-hand term of the equation system, including source-sink items, displacement boundary conditions and stress Boundary conditions;

Solve the coupled large-scale equations to obtain the macroscopic large-scale solution of the coarse grid unit, including large-scale displacement u ^c , large-scale pressure p ^c , and large-scale velocity v ^c .

The specific steps of obtaining the small-scale solution of the fine grid unit described in step S6 include:

Construct mapping matrices N _u , N _p , N _v , where N _u is a matrix of all multi-scale displacement basis functions as column vectors, and the multi-scale displacement basis functions correspond to each coarse grid unit in the multi-grid system The multi-scale displacement basis function of , N _p is a matrix with all the multi-scale pressure basis functions as column vectors, and the multi-scale pressure basis function is the multi-scale pressure basis function corresponding to each coarse grid unit in the multi-grid system, _Nv is a matrix with all multiscale velocity basis functions as column vectors, and the multiscale velocity basis function is a multiscale pressure basis function corresponding to each coarse grid boundary in the multigrid system;

According to the mapping matrix, the corresponding relationship between the macroscopic large-scale solution and the small-scale solution is: u ^f =N _u u ^c , p ^f ≈Ip ^c +N _p D _λ v ^c , v ^f =N _v v ^c , combined with the macroscopic large-scale solution of the coarse grid unit, the small-scale solution of the fine grid unit is obtained, where u ^f , p ^f , and v ^f represent the small-scale displacement, small-scale pressure and small-scale velocity respectively, and I is the identity matrix, D _λ is the mobility coefficient matrix, the macroscopic large-scale solution is the solution corresponding to the coarse grid, and the small-scale solution is the solution corresponding to the fine grid.

Fig. 4 is a flowchart of another embodiment of a fluid-solid coupling multiscale flow simulation method for elastic media provided by the present invention. As shown in Fig. 4, as another possible implementation mode, according to the actual situation of the reservoir, the obtained Seepage and stress parameters of elastically variable media in the reservoir, establish a seepage-stress coupling model, and perform multi-scale grid division on the seepage-stress coupling model, establish a multi-scale grid system, and then based on the multi-scale grid system, Establish the momentum conservation equation and the mass conservation equation, and use the multi-scale finite element method to solve the momentum conservation equation, and use the multi-scale simulation finite difference method to solve the mass conservation equation to obtain multi-scale basis functions, including multi-scale displacement basis functions and multi-scale pressure basis functions. function and multi-scale displacement basis function, and then construct a stiffness matrix based on the multi-scale basis function to solve the coarse grid, including coarse-grid displacement solution and coarse-grid pressure solution, according to the displacement and The mapping relationship of the pressure solution, the fine grid displacement solution and the fine grid pressure solution are carried out.

In this paper, specific examples are used to illustrate the principle and implementation of the invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. The described embodiments are only part of the embodiments of the present invention. , not all of the embodiments, based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work, all belong to the protection scope of the present invention.

Claims (4)

1. A fluid-solid coupling multi-scale flow simulation method for elastic media, characterized in that, comprising the steps of: Obtain geological parameters and mechanical parameters of the reservoir, and establish a geometric model of the reservoir; Perform multi-scale grid division on the reservoir geometry model to obtain a multi-scale grid system including coarse grid subsystem and fine grid subsystem; Based on the multi-scale grid system, the local flow region is selected, the local momentum conservation equation of the flow region is established, and the multi-scale finite element method is used to solve the local momentum conservation equation to obtain the multi-scale displacement basis function. The specific steps include: Considering each coarse grid unit as a local flow region Ω, the momentum conservation equation of the local flow region is established: ▽·(C _dr ▽ ^s u-bpI)＝0 onΩ×l (1) Among them, C _dr is the elastic tensor, l is the time interval l=[0,t], u and p represent the displacement vector and pressure respectively, I is the identity matrix, b is the Biot coefficient, ▽ ^s is the symmetric gradient operator; Select the boundary condition φ ⁱ (xj) = δ _ij , δ _ij is the Kronecker symbol, use the multi-scale finite element method to solve the local momentum conservation equation, and obtain the multi-scale displacement basis function of each coarse grid unit And construct the multi-scale displacement basis function matrix in is a small-scale displacement basis function, the small-scale displacement basis function is the basis function selected by the displacement variable when performing fine-grid calculations, φ _i ^u is the displacement on the i-th fine-grid node in the coarse-grid unit discrete value, is the number of fine grid unit nodes in the coarse grid unit; Based on the multi-scale grid system, select the flow area, establish the local mass conservation equation of the flow area, use the multi-scale simulation finite difference method to solve the local mass conservation equation, and obtain the multi-scale velocity basis function and multi-scale pressure basis function, the specific steps include: Two adjacent coarse grid cells are regarded as a flow region Ω' to ensure local conservation, and the local mass conservation equation of the flow region is established: Among them, b is the Biot coefficient, l is the time interval l=[0,t], M _b is the Biot modulus, is the derivative of displacement with respect to time, is the derivative of pressure with respect to time, λ is the fluid flow coefficient, and f is the source-sink term; Select closed boundary conditions, use the multi-scale simulation finite difference method to solve the local mass conservation equation, and obtain the multi-scale pressure basis function corresponding to each coarse grid cell Multiscale velocity basis functions corresponding to each coarse grid boundary And construct the multiscale pressure basis function matrix and the multiscale velocity basis function matrix in, and are the small-scale pressure basis function and the small-scale velocity basis function respectively, the small-scale pressure basis function is the basis function of the pressure variable when the fine-grid calculation is performed, and the small-scale velocity basis function is the basis function of the fine-grid calculation When , the basis function of the velocity variable, is the discrete value of pressure on the boundary of the ith fine grid in the coarse grid unit, φ _i ^v is the discrete value of velocity on the boundary of the ith fine grid in the coarse grid unit, is the number of fine grid units in the coarse grid unit; is the number of boundaries of the fine grid unit in the coarse grid unit; Based on the multi-scale principle and multi-scale displacement basis function, multi-scale velocity basis function and multi-scale pressure basis function, the macro-large-scale solution of the coarse grid unit is obtained, and the mapping relationship between the macro-large-scale solution and the small-scale solution is obtained; According to the macroscopic large-scale solution and the mapping relationship between the large-scale solution and the small-scale solution, the small-scale solution of the fine grid unit is obtained. The specific steps include: constructing the mapping matrix N _u , N _p , N _v , where Nu _is Take all multiscale displacement basis functions as a matrix of column vectors, N _p take all multiscale pressure basis functions as a matrix of column vectors, and N _v take all multiscale velocity basis functions as a matrix of column vectors; According to the mapping matrix, the corresponding relationship between the macroscopic large-scale solution and the small-scale solution is: u ^f =N _u u ^c , p ^f ≈Ip ^c +N _p D _λ v ^c , v ^f =N _v v ^c , combined with the macroscopic large-scale solution of the coarse grid unit, obtains the small-scale solution of the fine grid unit, where u ^f , p ^f , and v ^f represent the small-scale displacement, small-scale pressure and small-scale velocity respectively, u ^c is the large-scale displacement, p ^c is the large-scale pressure, v ^c is the large-scale velocity, I is the identity matrix, and D _λ is the fluidity coefficient matrix. 2. The fluid-solid coupling multi-scale flow simulation method of an elastic medium according to claim 1, wherein the specific steps of the multi-scale grid division include: According to the size of the research area, determine the large-scale coarse grid step size and quantity in each spatial direction, and use the orthogonal grid to divide the reservoir geometric model into a small-scale fine grid to obtain a fine grid subsystem; Constructing a coarse grid subsystem using a load balancing algorithm on the basis of the fine grid, wherein the coarse grid units in the coarse grid subsystem are formed by interconnecting the fine grid units in the fine grid subsystem; A multi-scale grid system is composed of the coarse grid subsystem and the fine grid subsystem. 3. A fluid-solid coupling multi-scale flow simulation method for elastic media according to claim 2, wherein the fine grid subsystem includes basic characteristic parameters and mechanical parameters of reservoir rocks and fluids. 4. The fluid-solid coupling multi-scale flow simulation method of an elastic medium according to claim 1, wherein the specific steps of obtaining the macroscopic large-scale solution of the coarse grid unit include: The multi-scale displacement basis function matrix, the multi-scale pressure basis function matrix and the multi-scale velocity basis function matrix are assembled into a mapping operator φ, which is Construct the large-scale stiffness matrix A=φA ^f φ ^T , where A ^f is the small-scale stiffness matrix, and the small-scale stiffness matrix is the stiffness matrix formed after discretizing the momentum conservation equation and the momentum conservation equation on the small-scale fine grid , the specific elements include the mechanical stiffness matrix, the simulation finite difference coefficient matrix and the compression term coefficient matrix, on this basis, a large-scale equation system Ax=B is formed, where B is the right-hand term of the equation system, including source-sink items, displacement boundary conditions and Stress boundary conditions; Solve the coupled large-scale equations to obtain the macroscopic large-scale solution of the coarse grid unit, including large-scale displacement u ^c , large-scale pressure p ^c , and large-scale velocity v ^c .