A three-dimensional pore numerical modeling method for porous materials considering pore characteristics

Abstract

The application discloses a three-dimensional pore numerical modeling method of porous materials considering pore characteristics, and comprises the following steps: S1, adopting a high-precision imaging device to perform tomography on the porous materials, and acquiring a three-dimensional pore and a parameter database thereof of the porous materials in a cross-scale manner; S2, after equivalent simplification of the three-dimensional pore and the parameter thereof in S1, analyzing size, orientation and distribution law of the topography characteristics of the pore; S3, resampling based on a probability density function of the distribution law of the pore parameter in S2, and regenerating pore parameters conforming to the distribution law; S4, performing a complex space transformation on the regenerated pore parameters in S3 by adopting linear matrix operation, and giving pore parameters compatible with a numerical grid model modeling software; and S5, constructing a numerical model of the porous materials in a defined domain based on the modeling software according to the compatible pore parameters in S4.

Description

Technical Field

[0001] This application relates to the field of three-dimensional modeling and numerical simulation of porous materials in geomechanics, and specifically to a three-dimensional pore numerical modeling method for porous materials that considers pore characteristics. Background Technology

[0002] The pore structure of porous materials directly affects their macroscopic and microscopic responses, including permeation, heat transfer, mechanics, and damage. Conventional testing methods struggle to visually observe the spatial morphology of closed pores and complex channels, and cannot accurately quantify microscopic parameters such as pore size distribution, pore connectivity, and tortuosity. Three-dimensional modeling enables non-destructive visualization and quantitative characterization of pore structure, establishing the intrinsic relationship between microscopic pore characteristics and macroscopic properties such as permeability, thermal conductivity, and mechanical strength, revealing the physicochemical mechanisms of material service processes. Furthermore, it revolutionizes the traditional trial-and-error R&D model, enabling forward design and reverse optimization of porous materials. It can also simulate pore evolution under extreme conditions such as high temperature, high pressure, and strong corrosion, overcoming the limitations of physical experiments due to limited conditions, high costs, and significant destructive impacts, providing digital support for theoretical model verification and research on new material mechanisms. Therefore, establishing a three-dimensional model that accurately reflects the statistical laws of pores and can be directly used for numerical simulation solutions is of great significance. Existing stochastic pore modeling methods mostly remain at the two-dimensional level, or the reconstructed three-dimensional pores fail to reflect the pore distribution laws of the original material. Furthermore, the ellipsoidal pore geometric parameters obtained from 3D pore reconstruction are incompatible with the mesh input parameter system of existing numerical modeling software, lacking a direct conversion interface between the two. Therefore, there is an urgent need for a complete modeling method that starts from pore extraction from CT scans, integrates pore parameter calculation, parameter statistical analysis and resampling, theoretical conversion of pore parameters, 3D geometric reconstruction, and mesh export, to provide technical support for related fields. Summary of the Invention

[0003] The purpose of this application is to provide a three-dimensional numerical modeling method for porous materials that considers porosity characteristics. The specific technical solution is as follows:

[0004] A three-dimensional pore numerical modeling method for porous materials considering pore characteristics includes: S1, using a high-precision imaging device to perform tomographic scanning on the porous material to obtain a database of three-dimensional pores and their parameters across scales; S2, after equivalent simplification of the three-dimensional pores and their parameters in S1, analyzing the distribution law of pore size, orientation, and morphological characteristics; S3, resampling based on the probability density function of the pore parameter distribution law in S2 to regenerate pore parameters that conform to the distribution law; S4, using linear matrix operations to perform complex spatial transformations on the regenerated pore parameters in S3 to provide pore parameters compatible with numerical mesh modeling software; S5, based on the compatible pore parameters in S4, constructing a numerical model of the porous material within a specified domain using modeling software.

[0005] S1 includes: S1.1, using industrial CT to perform non-destructive scanning of porous materials, obtaining 3D CT grayscale images of the porous materials, and preprocessing them; S1.2, based on the preprocessed grayscale images in S1.1, using the top-hat algorithm, interactive threshold segmentation, and watershed algorithm with labeling to extract macro- and micro-pores from the rock core; S1.3, equating the pores in S1.2 to ellipsoids, using spatial and graphical computation methods to calculate the moment of inertia of the pores, thereby determining the principal axes of the equivalent ellipsoid, and calculating the lengths a, b, and c of the three principal axes of the ellipsoid; S1.4, based on the lengths a, b, and c of the three principal axes in S1.3, calculating the orientation of the pore principal axes. , , , , as well as In order to obtain a three-dimensional database of the porous material's pore size and parameters across scales.

[0006] The preprocessing in S1.1 includes: S1.11, using digital image technology to correct ray hardening and ring artifacts in the grayscale image; S1.12, using Gaussian filtering and median filtering to perform denoising and smoothing on the corrected grayscale image in S1.11.

[0007] When calculating the orientation of the pore principal axis in S1.4, and These are the angles between the principal axis a, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, respectively, and the x-axis. and These are the angles between the principal axis b, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, respectively, and the x-axis. and These represent the angles between the principal axis c, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, and the x-axis, respectively; and the shape factor of the pore. Expressed as:

[0008] ,

[0009] in, and These are the surface area and volume of the pores, respectively, obtained by statistically analyzing the surface area and volume of the voxel set that constitutes the pores.

[0010] S2 includes: S2.1, summarizing the pore size parameters of the three-dimensional pores and their parameters in S1, specifically including: the principal axis lengths a, b, and c of the equivalent ellipsoid; and the azimuth angles of the three principal axes a, b, and c of the equivalent ellipsoid. , , , , as well as Pore ​​morphology factor S2.1 is used to characterize the morphological complexity of pores; S2.2, the 10 datasets formed by the 10 parameters summarized in S2.1 are used to remove outliers of pores by logical AND condition judgment, combined with the actual scanned sample size and CT scan spatial resolution; S2.3, based on S2.2, the probability density distribution of each parameter in its reasonable distribution range is statistically analyzed.

[0011] S3 includes:

[0012] S3.1. Based on the probability density distribution of each parameter in S2.3 within its reasonable distribution range, the distribution law of the pore parameters is fitted using the kernel density estimation function, expressed as:

[0013] ,

[0014] in, The number of pore sample points. The bandwidth estimated by the kernel function. For kernel function, These are sample points.

[0015] S3.2, through The integral operation calculates the probability distribution function of pore parameters. , expressed as:

[0016] ,

[0017] Used The inverse transform sampling is used to obtain the regenerated pore parameters.

[0018] S4 includes:

[0019] S4.1, Using the principal axis azimuth angle , , , , as well as Calculate the principal axis direction vectors of the ellipsoid , as well as , expressed as:

[0020] ,

[0021] ,

[0022] .

[0023] S4.2, the direction vector in S4.1 , as well as Normalized to unit direction vector , as well as , expressed as:

[0024] ,

[0025] ,

[0026] .

[0027] S4.3. The Gram-Schmidt orthogonalization method is used to orthogonalize the unit direction vectors in S4.2 to obtain strictly orthogonal ellipsoidal principal axis direction vectors. , as well as , expressed as:

[0028] ,

[0029] ,

[0030] .

[0031] S4.4, based on the orthogonal ellipsoidal principal axis direction vectors in S4.3 , as well as Construct rotation matrix , expressed as:

[0032] .

[0033] S4.5 Calculate the rotation matrix in S4.4 The determinant of the matrix is ​​such that when the determinant is negative, one of the direction vectors is inverted to ensure that the rotation matrix satisfies the right-hand rule; the right-hand rule correction condition is expressed as:

[0034] .

[0035] S4.6, Calculate the rotation matrix traces To find the rotation angle ,trace The calculation formula is:

[0036] ,

[0037] Rotation angle The calculation formula is:

[0038] ,

[0039] .

[0040] S4.7. The direction vector of the rotation axis is obtained by finding the characteristic equation of the rotation matrix, expressed as:

[0041] ,

[0042] ,

[0043] in, It is the identity matrix. is the direction vector of the rotation axis.

[0044] S4.8, Preserve the rotation axis, rotation angle, and center coordinates of the ellipsoidal aperture. , , }, { , , }, }

[0045] S5 includes: S5.1 Establishing an external domain based on the required numerical simulation sample type, which can be a cuboid domain or a cylindrical domain; S5.2 Calculating the axis-aligned enclosure size of the ellipsoid in the global coordinate system based on the resampled semi-axis length and direction vector; S5.3 Randomly generating pore center coordinates within the external domain; S5.4 Determining whether the generated pores are completely located within the external domain based on boundary constraints; S5.5 Performing overlap determination based on the pore center spacing and pore geometry, and eliminating candidate pores that overlap with the generated pores; S5.6 Retaining the center coordinates and regenerated pore parameters of pores that satisfy boundary constraints and non-overlapping constraints, and writing them into the Gmsh script to construct a porous numerical mesh model.

[0046] S5.6 includes: S5.61, creating a unit sphere in the Gmsh script; S5.62, scaling the unit sphere proportionally to an ellipsoid in the Gmsh script based on the three principal axis lengths a, b, and c of the regenerated ellipsoidal aperture; S5.63, based on the orientation of the three principal axes of the regenerated aperture. , , , , as well as Calculate the rotation axis and rotation angle, and perform a rotation transformation on the ellipsoid in the Gmsh script; S5.64, perform a translation transformation in the Gmsh script based on the coordinates of the regenerated ellipsoid's pore center, moving the rotated ellipsoid from the origin to the target center coordinates; S5.65, iteratively generate the geometry of all pore ellipsoids; S5.66, use Boolean difference operations to subtract all pore ellipsoids from the outer domain to form a three-dimensional porous material geometric model; S5.67, calculate the maximum and minimum feature dimensions in the ellipsoid set, set appropriate mesh sizes to generate a three-dimensional mesh; S5.68, finally export .geo, .msh, and .inp files containing geometric and mesh information.

[0047] The beneficial effects of this application are that it constructs a complete technical chain from CT scan pore extraction, pore parameter statistical analysis, kernel density estimation (KDE) resampling generation, three-dimensional direction vector, construction of rotation matrix and rotation parameter solution, to geometric modeling and mesh export in Gmsh software, realizing the extension from "two-dimensional pore random model generation" to "automatic construction of three-dimensional random mesh model". At the same time, by introducing direction vector normalization, Gram-Schmidt orthogonalization, right-hand system correction and rotation axis angle solution methods, it solves the problems of complex spatial orientation and unstable geometric transformation of three-dimensional ellipsoidal pores. Furthermore, it directly embeds the regenerated pores into the domain and exports mesh files that can be used in numerical simulation software such as finite element method, improving the realism, automation and engineering applicability of numerical modeling of porous materials. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the application process.

[0049] Figure 2 A schematic diagram for calculating the lengths a, b, and c of the three principal axes of the ellipsoid;

[0050] Figure 3 This is a frequency distribution histogram based on probability density.

[0051] Figure 4 This is a schematic diagram illustrating the process of the modeling software in this application constructing a numerical model of a porous material within a specified domain;

[0052] Figure 5 This is a schematic diagram illustrating the generation of a 3D mesh by setting appropriate mesh sizes to calculate the maximum and minimum feature dimensions in the ellipsoid set. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this application. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0054] like Figure 1 As shown, a three-dimensional pore numerical modeling method for porous materials considering pore characteristics includes:

[0055] S1. High-precision imaging equipment is used to perform tomographic scanning of the porous material to obtain a three-dimensional database of its pore size and parameters across multiple scales. Specifically, this includes:

[0056] S1.1. Industrial CT is used to perform non-destructive scanning of porous materials to obtain three-dimensional CT grayscale images of the porous materials, which are then preprocessed. In this application, the preprocessing includes: S1.11. Digital image processing technology is used to correct ray hardening and ring artifacts in the grayscale image; S1.12. Gaussian filtering and median filtering are used to denoise and smooth the corrected grayscale image from S1.11.

[0057] S1.2. Based on the preprocessed grayscale image in S1.1, the macro- and micro-pores of the rock core are extracted using the top-hat algorithm, interactive threshold segmentation, and watershed algorithm with labeling.

[0058] S1.3. The pores in S1.2 are equivalent to ellipsoids. Spatial and graphical calculation methods are used to calculate the moment of inertia of the pores, thereby determining the principal axes of the equivalent ellipsoid, and calculating the lengths a, b and c of the three principal axes of the ellipsoid.

[0059] S1.4. Based on the lengths a, b, and c of the three principal axes in S1.3, calculate the orientation of the pore principal axes. , , , , as well as This allows for the acquisition of a three-dimensional database of pore size and parameters across different scales for the porous material. In applications, when calculating the orientation of the principal pore axes... and These are the angles between the principal axis a, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, respectively, and the x-axis. and These are the angles between the principal axis b, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, respectively, and the x-axis. and These represent the angles between the principal axis c, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, and the x-axis, respectively; and the shape factor of the pore. Expressed as:

[0060] ,

[0061] in, and The surface area and volume of the pores are obtained by statistically analyzing the surface area and volume of the voxel set constituting the pores. Furthermore, abnormal pores in the 3D pore model are removed to obtain a valid pore set for parameter statistics.

[0062] like Figure 2 As shown in Figure S2, after equivalent simplification of the three-dimensional pores and their parameters in S1, the distribution patterns of pore size, orientation, and morphological characteristics are analyzed. Specifically, this includes:

[0063] S2.1. Summarize the pore size parameters of the three-dimensional pores and their parameters in S1, specifically including: the principal axis lengths a, b, and c of the equivalent ellipsoid; and the azimuth angles of the three principal axes a, b, and c of the equivalent ellipsoid. , , , , as well as Pore ​​morphology factor It is used to characterize the morphological complexity of pores.

[0064] S2.2. For the 10 datasets formed by the 10 parameters summarized in S2.1, outliers with pores are eliminated by logical AND condition judgment, combined with the actual sample size and CT scan spatial resolution.

[0065] S2.3. Based on S2.2, statistically analyze the probability density distribution of each parameter within its reasonable distribution range.

[0066] like Figure 3 As shown, S3 resamples the pore parameter distribution based on the probability density function in S2 to regenerate pore parameters that conform to this distribution. Specifically, this includes:

[0067] S3.1. Based on the probability density distribution of each parameter in S2.3 within its reasonable distribution range, the distribution law of the pore parameters is fitted using the kernel density estimation function, expressed as:

[0068] ,

[0069] in, The number of pore sample points. The bandwidth estimated by the kernel function. For kernel function, These are the sample points. In the application, based on the distribution law of pore parameters and the fitting effect, a suitable kernel function in the KDE function is selected; according to preliminary test results, the Gaussian kernel function shows better fitting effect for the pore parameter distribution of lattice and gravel structure reef limestone. The formula for the Gaussian kernel function is:

[0070] .

[0071] S3.2, through The integral operation calculates the probability distribution function of pore parameters. , expressed as:

[0072] ,

[0073] Used The inverse transform sampling is used to obtain the regenerated pore parameters. In application, the probability distribution function of the pore parameters is obtained by integrating the optimized KDE kernel density function. ; the probability distribution function Normalize to the [0, 1] interval, and generate uniformly distributed random samples within the [0, 1] interval; map the generated random samples to the density distribution of the original data through interpolation to obtain the regenerated pore parameters.

[0074] S4. A complex spatial transformation is performed on the regenerated pore parameters in S3 using linear matrix operations, resulting in pore parameters compatible with numerical grid modeling software. Specifically, this includes:

[0075] S4.1, Using the principal axis azimuth angle , , , , as well as Calculate the principal axis direction vectors of the ellipsoid , as well as , expressed as:

[0076] ,

[0077] ,

[0078] .

[0079] S4.2, the direction vector in S4.1 , as well as Normalized to unit direction vector , as well as , expressed as:

[0080] ,

[0081] ,

[0082] .

[0083] S4.3. The Gram-Schmidt orthogonalization method is used to orthogonalize the unit direction vectors in S4.2 to obtain strictly orthogonal ellipsoidal principal axis direction vectors. , as well as , expressed as:

[0084] ,

[0085] ,

[0086] .

[0087] S4.4, based on the orthogonal ellipsoidal principal axis direction vectors in S4.3 , as well as Construct rotation matrix , expressed as:

[0088] .

[0089] S4.5 Calculate the rotation matrix in S4.4 The determinant of the matrix is ​​such that when the determinant is negative, one of the direction vectors is inverted to ensure that the rotation matrix satisfies the right-hand rule; the right-hand rule correction condition is expressed as:

[0090] .

[0091] S4.6, Calculate the rotation matrix traces To find the rotation angle ,trace The calculation formula is:

[0092] ,

[0093] Rotation angle The calculation formula is:

[0094] ,

[0095] .

[0096] S4.7. The direction vector of the rotation axis is obtained by finding the characteristic equation of the rotation matrix, expressed as:

[0097] ,

[0098] ,

[0099] in, It is the identity matrix. is the direction vector of the rotation axis.

[0100] S4.8, Preserve the rotation axis, rotation angle, and center coordinates of the ellipsoidal aperture. , , }, { , , }, }

[0101] like Figure 4 As shown, S5, based on the pore parameters compatible with those in S4, constructs a numerical model of the porous material within a specified domain using modeling software. Specifically, this includes:

[0102] S5.1 Establish an external domain according to the required numerical simulation sample type. The external domain can be a cuboid domain or a cylindrical domain.

[0103] S5.2 Calculate the axis-aligned bounding size of the ellipsoid in the global coordinate system based on the resampled semi-axis length and direction vector.

[0104] S5.3 Randomly generate pore center coordinates within the external domain.

[0105] S5.4 Determine whether the generated pores are completely located within the external domain based on the boundary constraints.

[0106] S5.5. Based on the center-to-center distance and geometric dimensions of the pores, overlap determination is performed, and candidate pores that overlap with the already generated pores are eliminated.

[0107] S5.6. For pores satisfying boundary constraints and non-overlapping constraints, retain their center coordinates and regenerated pore parameters, and write them into the Gmsh script to construct a porous numerical mesh model. Specifically, this includes: S5.61. Creating a unit sphere in the Gmsh script; S5.62. Scaling the unit sphere to an ellipsoid in the Gmsh script according to the three principal axis lengths a, b, and c of the regenerated ellipsoidal pores; S5.63. Scaling the ellipsoid to an ellipsoid according to the three principal axis orientations of the regenerated pores. , , , , as well as Calculate the rotation axis and rotation angle, and perform a rotation transformation on the ellipsoid in the Gmsh script; S5.64, perform a translation transformation in the Gmsh script based on the coordinates of the regenerated ellipsoid's pore center, moving the rotated ellipsoid from the origin to the target center coordinates; S5.65, iteratively generate the geometry of all pore ellipsoids; S5.66, use Boolean difference operations to subtract all pore ellipsoids from the outer domain, forming a three-dimensional porous material geometric model; Figure 5 As shown in Figure 5.67, calculate the maximum and minimum feature dimensions in the ellipsoid set, set an appropriate mesh size to generate a 3D mesh; and finally, export the .geo, .msh, and .inp files containing geometric and mesh information.

Claims

1. A three-dimensional numerical modeling method for porous materials considering pore characteristics, characterized in that, include: S1. Use high-precision imaging equipment to perform tomographic scanning on porous materials to obtain a three-dimensional database of the porous material's pore size and parameters across scales; S2. After simplifying the three-dimensional pores and their parameters in S1, analyze the distribution law of pore size, orientation and morphological characteristics. S3. Based on the probability density function of the pore parameter distribution law in S2, resample and regenerate pore parameters that conform to the distribution law; S4. Perform complex spatial transformations on the regenerated pore parameters in S3 using linear matrix operations to provide pore parameters compatible with numerical grid modeling software. S5. Based on the pore parameters compatible in S4, construct a numerical model of the porous material within the specified domain using modeling software.

2. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 1, characterized in that, S1 includes: S1.

1. Use industrial CT to perform non-destructive scanning on porous materials, obtain three-dimensional CT grayscale images of porous materials, and perform preprocessing. S1.2 Based on the preprocessed grayscale image in S1.1, the macro-micro porosity of the rock core is extracted using the top-hat algorithm, interactive threshold segmentation, and watershed algorithm with labeling. S1.

3. The pores in S1.2 are equivalent to ellipsoids. Spatial and graphical calculation methods are used to calculate the moment of inertia of the pores, thereby determining the principal axes of the equivalent ellipsoid, and calculating the lengths a, b and c of the three principal axes of the ellipsoid. S1.

4. Based on the three main shaft lengths a, b, and c in S1.3, calculate the orientation of the pore main shaft. , , , , as well as In order to obtain a three-dimensional database of the porous material's pore size and parameters across scales.

3. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 2, characterized in that, The preprocessing in S1.1 includes: S1.

11. Digital image technology is used to correct the ray hardening and ring artifact phenomena in grayscale images; S1.

12. The grayscale image corrected in S1.11 is subjected to noise reduction and smoothing processing using Gaussian filtering and median filtering.

4. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 3, characterized in that, When calculating the orientation of the pore principal axis in S1.4, and These are the angles between the principal axis a, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, respectively, and the x-axis. and These are the angles between the principal axis b, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, respectively, and the x-axis. and These represent the angles between the principal axis c, the z-axis in the Cartesian coordinate system, and the projection of the z-axis onto the xy-plane, and the x-axis, respectively; and the shape factor of the pore. Expressed as: ， in, and These are the surface area and volume of the pores, respectively, obtained by statistically analyzing the surface area and volume of the voxel set that constitutes the pores.

5. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 4, characterized in that, S2 includes: S2.1 Summarize the pore size parameters of the three-dimensional pores and their parameters in S1, specifically including: The principal axis lengths a, b, and c of the equivalent ellipsoid; Azimuth angles of the three principal axes a, b, and c of the equivalent ellipsoid , , , , as well as ; Pore ​​morphology factor , used to characterize the morphological complexity of pores; S2.

2. For the 10 datasets formed by the 10 parameters summarized in S2.1, outlier values ​​of pores are eliminated by logical AND condition judgment, combined with the actual scanned sample size and CT scan spatial resolution. S2.

3. Based on S2.2, statistically analyze the probability density distribution of each parameter within its reasonable distribution range.

6. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 5, characterized in that, S3 includes: S3.1 Based on the probability density distribution of each parameter in S2.3 within its reasonable distribution range, the distribution law of the pore parameters is fitted using a kernel density estimation function, expressed as: ， in, The number of pore sample points. The bandwidth estimated by the kernel function. For kernel function, For sample points; S3.2, through The integral operation calculates the probability distribution function of pore parameters. , expressed as: ， Used The inverse transform sampling is used to obtain the regenerated pore parameters.

7. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 6, characterized in that, S4 includes: S4.1, Using the principal axis azimuth angle , , , , as well as Calculate the principal axis direction vectors of the ellipsoid , as well as , expressed as: ， ， ； S4.2, the direction vector in S4.1 , as well as Normalized to unit direction vector , as well as , expressed as: ， ， ； S4.

3. The unit direction vector in S4.2 is orthogonalized using the Gram-Schmidt orthogonalization method to obtain strictly orthogonal ellipsoidal principal axis direction vectors. , as well as , expressed as: ， ， ； S4.4, Based on the orthogonal ellipsoidal principal axis direction vectors in S4.3 , as well as Construct rotation matrix , expressed as: ； S4.5 Calculate the rotation matrix in S4.

4. The determinant of the matrix is ​​such that when the determinant is negative, one of the direction vectors is inverted to ensure that the rotation matrix satisfies the right-hand rule; the right-hand rule correction condition is expressed as: ； S4.6, Calculate the rotation matrix traces To find the rotation angle ,trace The calculation formula is: ， Rotation angle The calculation formula is: ， ； S4.

7. The direction vector of the rotation axis is obtained by finding the characteristic equation of the rotation matrix, expressed as: ， ， in, It is the identity matrix. The direction vector of the rotation axis; S4.8, Preserve the rotation axis, rotation angle, and center coordinates of the ellipsoidal aperture. , , }, { , , }, } 8. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 7, characterized in that, S5 includes: S5.1 Establish an external domain according to the required numerical simulation sample type. The external domain can be a cuboid domain or a cylindrical domain. S5.2 Calculate the axis-aligned bounding size of the ellipsoid in the global coordinate system based on the resampled semi-axis length and direction vector; S5.3 Randomly generate pore center coordinates within the external domain; S5.4 Determine whether the generated pores are completely located within the external domain based on the boundary constraints; S5.

5. Based on the center-to-center distance and geometric dimensions of the pores, determine the overlap and remove candidate pores that overlap with the already generated pores. S5.

6. For pores that satisfy boundary constraints and non-overlapping constraints, retain their center coordinates and regenerated pore parameters, and write them into the Gmsh script to construct a porous numerical mesh model.

9. The three-dimensional pore numerical modeling method for porous materials considering pore characteristics as described in claim 8, characterized in that, S5.6 includes: S5.

61. Create a unit sphere in the Gmsh script; S5.

62. Based on the three principal axis lengths a, b, and c of the regenerated ellipsoidal aperture, scale the unit sphere proportionally into an ellipsoid in the Gmsh script. S5.63, Based on the three principal axis orientations of the regenerated pores , , , , as well as Calculate the rotation axis and rotation angle, and perform a rotation transformation on the ellipsoid in the Gmsh script; S5.

64. Based on the coordinates of the regenerated ellipsoid pore center, perform a translation transformation in the Gmsh script to move the rotated ellipsoid from the origin to the target center coordinates. S5.65, Cyclicly generate all pore ellipsoidal geometries; S5.

66. Subtract all the pore ellipsoids from the outer domain using Boolean difference operations to form a three-dimensional porous material geometric model; S5.67 Calculate the maximum and minimum feature dimensions in the ellipsoid set, and set an appropriate mesh size to generate a three-dimensional mesh; S5.68 Finally, export the .geo, .msh, and .inp files containing geometric and mesh information.

Images