Adaptive height anisotropic mesh generation method, system, device and medium

Abstract

The application discloses an adaptive height anisotropic mesh generation method, system, device and medium, and the method comprises the following steps: initializing the array surface data of an object; determining whether there is a pushable array surface in the array surface data; if there is a pushable array surface, calculating the normal of the array surface, calculating the pushing direction of the array surface node according to the normal of the array surface, iteratively optimizing the pushing direction of the array surface node, and obtaining the pushing direction of the array surface node; calculating the pushing step length of each array surface node, and generating anisotropic units by pushing each array surface according to the pushing direction and the pushing step length of the array surface node; determining whether the generated anisotropic units meet the early stop condition; until there is no pushable array surface; taking all the unpushable array surfaces as the initial boundary of the isotropic mesh generation, and generating the isotropic mesh of the remaining space by using the isotropic mesh generation method. The application can generate smooth transition, highly adaptive anisotropic mesh on any specified boundary.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mesh generation, in particular to a self-adaptive height anisotropic mesh generation method, system, device and medium. BACKGROUND

[0002] In the numerical simulation of computational fluid dynamics of high Reynolds number flow, in order to accurately simulate the viscous boundary layer near the surface of the object, it is necessary to generate slender boundary layer mesh in the boundary layer. The boundary layer mesh is large in scale in the flow direction and small in scale in the flow normal direction, so as to accurately analyze the large normal gradient in the boundary layer, and the anisotropic flow characteristics directly determine that the grid scale also has anisotropic geometric characteristics.

[0003] At the same time, the anisotropic mesh near the object surface and the isotropic mesh unit scale far from the object surface must be smooth to reduce the numerical error of numerical simulation, and the generation of anisotropic mesh capable of smooth transition near the object surface is crucial to the simulation accuracy of boundary layer flow. SUMMARY

[0004] In view of this, the present application provides a self-adaptive height anisotropic mesh generation method, system, device and medium, aiming at solving the problem of non-smooth transition of anisotropic mesh and free flow area mesh, low mesh quality in the prior art.

[0005] The present application discloses a self-adaptive height anisotropic mesh generation method, which comprises:

[0006] Step 1: initializing the surface data of the object; the surface is the boundary line segment of the object in two-dimensional case, and is the triangular face mesh or quadrilateral face mesh of the object in three-dimensional case; the object is a two-dimensional / three-dimensional geometric entity including multiple components; the components of the object include the fuselage, the wing and the engine of the aircraft;

[0007] Step 2: judging whether there is a pushable surface in the surface data, if there is a pushable surface, calculating the normal of the surface, calculating the push direction of the surface node according to the normal of the surface, iteratively optimizing the push direction of the surface node to obtain the push direction of the surface node; calculating the push step of each surface node, and generating anisotropic elements by pushing each surface according to the push direction and the push step of the surface node;

[0008] Step 3: judging whether the generated anisotropic elements meet the early stop condition, if the early stop condition is met, updating the surface data; the early stop condition includes the geometric early stop and the adjacent condition early stop;

[0009] Step 4: Repeat steps 2 to 3 until there are no more advanceable surfaces; use all non-advanceable surfaces as the initial boundary for isotropic mesh generation, and use the isotropic mesh generation method to generate the isotropic mesh for the remaining space.

[0010] Furthermore, in step 2, in the two-dimensional case, the front surface node is the endpoint of a line segment, and in the three-dimensional case, the front surface node is the vertex of a triangular or quadrilateral mesh. The front surface node has physical coordinates, which correspond to discrete calculation points in the flow field solver; the propulsion direction is a spatial vector used to control the mesh growth direction.

[0011] Furthermore, step 3 also includes:

[0012] If the generated anisotropic elements meet the early stopping condition, the current array surface stops early and will no longer be used to advance the generation of anisotropic meshes. Steps 2 to 3 are repeated until there are no more array surfaces to advance.

[0013] Furthermore, in step 3, geometric early stopping is related to the quality of the new cell, the current layer number, the cell size, and the cell aspect ratio; proximity condition early stopping is related to the set safety distance and the candidate array search range; both the safety distance and the candidate array search range are related to the advance step size.

[0014] Furthermore, the step of using all non-advanceable front surfaces as the initial boundary for isotropic mesh generation, and generating the isotropic mesh for the remaining space using an isotropic mesh generation method, includes:

[0015] Step 41: Use the specified geometric boundary as the initial front surface for advancement to generate anisotropic meshes at the specified geometric boundary;

[0016] Step 42: Match the nodes of the anisotropic mesh output in Step 41 with other boundaries: Set the boundary flag to be enabled in the component parameters, mark the mesh line connector or mesh surface domain to generate the anisotropic mesh, and mark the mesh line connector or mesh surface domain to be matched with the boundary layer; the component to be matched needs to enable boundary matching in the component parameters.

[0017] Step 43: Perform node matching using either the pre-discrete matching method or the projection reconstruction matching method. Pre-discrete matching method: Based on the boundary layer generation parameters for matching, re-discrete the geometric lines bound to the mesh line Connector or mesh surface Domain to form new mesh lines or mesh surfaces that replace the original mesh lines or mesh surfaces and use them as the initial boundary surface to advance the generation of anisotropic meshes. Parameters include the first layer height, growth rate, and number of layers. Projection reconstruction matching method: Advance the generation of anisotropic meshes, marking the nodes that need to be matched during the generation process. After the anisotropic mesh generation is complete, project the marked network nodes onto the matching geometric boundary, and reconstruct the matching boundary distribution based on the projection.

[0018] Further, step 42 includes:

[0019] Establish a hierarchical data structure between Part, Edge, Face, Connector, and Domain. Bind the geometry to the grid line, the geometry to the grid face, and the grid generation parameters to the part to enable the generation of anisotropic meshes for any specified part.

[0020] Further, see Figure 4 The method for generating anisotropic meshes by specifying arbitrary components includes:

[0021] Start mesh generation, traverse all parts, determine whether the current part has boundary layer mesh generation enabled, if boundary layer mesh generation is enabled, read the boundary layer parameter BoundaryLayerParams, obtain the associated geometric boundary GeomBoundary, start from the boundary, apply the boundary layer generation parameters to advance the generated network, check for early stopping conditions, until the anisotropic mesh generation ends; the parameters include the first layer height, the number of layers, and the growth rate.

[0022] This application also discloses an adaptive height anisotropic mesh generation system, which implements the above-described adaptive height anisotropic mesh generation method, comprising:

[0023] The initialization module is used to initialize the surface data of an object; the surface is the boundary line segment of the object in two dimensions, and the triangular or quadrilateral surface mesh of the object in three dimensions; the object is a two-dimensional / three-dimensional geometric entity that includes multiple parts; the parts of the object include the fuselage, wings, and engines of the passenger aircraft;

[0024] The first judgment module is used to determine whether there is a pushable array in the array data. If there is a pushable array, the normal of the array is calculated. Based on the normal of the array, the push direction of the array node is calculated. The push direction of the array node is iteratively optimized to obtain the push direction of the array node. The push step size of each array node is calculated. Based on the push direction and push step size of the array node, anisotropic elements are generated by pushing the array one by one.

[0025] The second judgment module is used to determine whether the generated anisotropic elements meet the early stopping condition. If the early stopping condition is met, the array data is updated. The early stopping condition includes geometric early stopping and proximity condition early stopping.

[0026] The mesh generation module is used to repeatedly run the first judgment module and the second judgment module until there are no more advanceable surfaces; all non-advanceable surfaces are used as the initial boundary for isotropic mesh generation, and isotropic meshes for the remaining space are generated using the isotropic mesh generation method.

[0027] This application also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executed by the processor, wherein the processor executes the computer program to implement the above-described method for generating anisotropic meshes with adaptive height.

[0028] This application also discloses a non-transitory computer-readable storage medium storing computer instructions for causing a computer to execute the above-described adaptive height anisotropic mesh generation method.

[0029] Due to the adoption of the above technical solution, this application has the following advantages:

[0030] 1. This application can generate smooth transition and highly adaptive anisotropic meshes on any specified boundary.

[0031] 2. Compared with traditional mesh generation methods and systems, this application achieves smoother transitions in mesh cell area / volume, improves the mass ratio of the largest adjacent cell volume by more than 50%, and improves the mesh equiangular distortion mass by more than 20%. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0033] Figure 1This is a flowchart illustrating an adaptive height anisotropic mesh generation method according to an embodiment of this application.

[0034] Figure 2 This is a schematic diagram of the geometric early stopping judgment process according to an embodiment of this application;

[0035] Figure 3 This is a schematic diagram of the proximity condition early stop judgment process in an embodiment of this application;

[0036] Figure 4 A schematic diagram illustrating the basic process of generating anisotropic meshes by specifying arbitrary boundaries for the implementation of embodiments of this application;

[0037] Figure 5(a) is a schematic diagram of the process of implementing boundary matching using the pre-discrete matching method in an embodiment of this application;

[0038] Figure 5(b) is a schematic diagram of the process of implementing boundary matching using the projection reconstruction matching method in an embodiment of this application;

[0039] Figure 6(a) is a schematic diagram of a height-adaptive and boundary-matched anisotropic mesh generation example of an embodiment of this application - a height-adaptive anisotropic mesh (two-dimensional three-segment airfoil);

[0040] Figure 6(b) is a schematic diagram of a height-adaptive and boundary-matched anisotropic mesh generation example of an embodiment of this application - a height-adaptive and boundary-matched anisotropic mesh (two-dimensional single-segment airfoil);

[0041] Figure 6(c) is a schematic diagram of a height-adaptive and boundary-matched anisotropic mesh generation example (3D passenger aircraft model) according to an embodiment of this application.

[0042] Figure 6(d) is a schematic diagram of a height-adaptive and boundary-matching anisotropic mesh generation example (3D passenger aircraft model) according to an embodiment of this application. Detailed Implementation

[0043] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only some, not all, of the embodiments of the present application. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.

[0044] See Figure 1 This application provides an embodiment of an adaptive height anisotropic mesh generation method, which includes:

[0045] Step 1: Initialize the surface data of the object; the surface is the boundary line segment of the object in two dimensions, and the triangular or quadrilateral surface mesh of the object in three dimensions; the object is a two-dimensional / three-dimensional geometric entity that includes multiple parts; the parts of the object include the fuselage, wings, and engines of the passenger aircraft;

[0046] Step 2: Determine whether there are advanceable front surfaces in the front surface data. If there are advanceable front surfaces, calculate the normal of the front surface. Based on the normal of the front surface, calculate the advance direction of the front surface nodes. The Laplace smoothing algorithm can be used to iteratively optimize the advance direction of the front surface nodes to obtain the advance direction of the front surface nodes. Calculate the advance step size of each front surface node. Based on the advance direction and advance step size of the front surface nodes, advance each front surface to generate anisotropic elements.

[0047] Step 3: Determine whether the generated anisotropic elements meet the early stopping condition. If the early stopping condition is met, update the array data. The early stopping condition includes geometric early stopping and proximity condition early stopping.

[0048] Step 4: Repeat steps 2 to 3 until there are no more advanceable surfaces; use all non-advanceable surfaces as the initial boundary for isotropic mesh generation, and use the isotropic mesh generation method to generate the isotropic mesh for the remaining space.

[0049] Optionally, in step 2, in the two-dimensional case, the front surface node is the endpoint of a line segment, and in the three-dimensional case, the front surface node is the vertex of a triangular or quadrilateral mesh. The front surface node has physical coordinates, which correspond to discrete calculation points in the flow field solver; the propulsion direction is a spatial vector used to control the mesh growth direction.

[0050] Optionally, step 3 further includes:

[0051] If the generated anisotropic elements meet the early stopping condition, the current array surface stops early and will no longer be used to advance the generation of anisotropic meshes. Steps 2 to 3 are repeated until there are no more array surfaces to advance.

[0052] Optionally, in step 3, geometric early stopping is related to the quality of the new cell, the current layer number, the cell size, and the cell aspect ratio; proximity condition early stopping is related to the set safety distance and the candidate array search range; both the safety distance and the candidate array search range are related to the advance step size.

[0053] Specifically, see Figure 2 Determine whether the generated anisotropic elements satisfy geometric early stopping, including:

[0054] Determine whether the anisotropic unit meets the first early stop condition. If it does, trigger early stop. If it does not meet the first early stop condition, continue to determine whether the second early stop condition is met.

[0055] If the second early stop condition is met, then early stop is triggered; if the second early stop condition is not met, then the process continues to determine whether the third early stop condition is met.

[0056] If the third early stop condition is met, then early stop is triggered; if the third early stop condition is not met, then continue to determine whether the fourth early stop condition is met.

[0057] If the fourth early stop condition is met, an early stop is triggered; if the fourth early stop condition is not met, the advance of the formation continues.

[0058] The first early stopping condition is that the quality of the new cell is lower than the quality threshold; the second early stopping condition is that the current layer number is greater than the total number of layers; the third early stopping condition is that the cell size is greater than m times the local grid scale; and the fourth early stopping condition is that the cell aspect ratio is less than n. m can be 1.3, and n can be 1.1.

[0059] See Figure 3 Determining whether the generated anisotropic elements satisfy the proximity condition for early stopping includes:

[0060] The safe distance between the newly generated array and other arrays is set to the product of the advance step size and a first specified value to ensure that the newly generated array does not intersect or collide with other arrays during the array advance process;

[0061] Within the candidate surface search range, a spatial tree data structure is used to search for surfaces that may collide, forming a list of possible collision surfaces; the candidate surface search range is the product of the advance step size and the second specified value; both the first and second specified values ​​are positive numbers; the first specified value can be 0.5, and the second specified value can be 3.0;

[0062] Check if there are any undetected arrays in the list of possible collision arrays. If so, check if the array is in the current propulsion direction of the propulsion array. If so, calculate the distance between arrays and check if the distance is less than the set safe distance. If it is less, there is an adjacent array, and early stop is triggered.

[0063] If there are no undetected arrays in the list of possible collision arrays, continue advancing the array; if the array is not in the advancing direction of the current advancing array, continue advancing the array; if the distance is greater than or equal to the set safety distance, continue advancing the array.

[0064] Optionally, the step of using all non-advanceable front surfaces as the initial boundary for isotropic mesh generation, and generating the isotropic mesh for the remaining space using an isotropic mesh generation method, includes:

[0065] Step 41: Use the specified geometric boundary as the initial front surface for advancement to generate anisotropic meshes at the specified geometric boundary;

[0066] Step 42: Match the nodes of the anisotropic mesh output in Step 41 with other boundaries: Set the boundary flag to be enabled in the component parameters, mark the mesh line connector or mesh surface domain to generate the anisotropic mesh, and mark the mesh line connector or mesh surface domain to be matched with the boundary layer; the component to be matched needs to enable boundary matching in the component parameters.

[0067] Step 43: Perform node matching using either the pre-discrete matching method or the projection reconstruction matching method; see Figure 5(a). Pre-discrete matching method: Based on the boundary layer generation parameters of the matching, re-discrete the geometric lines bound to the mesh line Connector or mesh surface Domain to form new mesh lines or mesh surfaces to replace the original mesh lines or mesh surfaces and use them as the initial boundary surface to advance the generation of anisotropic meshes; the parameters include the first layer height, growth rate, and number of layers; see Figure 5(b). Projection reconstruction matching method: Advance the generation of anisotropic meshes, mark the nodes that need to be matched during the generation of anisotropic meshes, and after the anisotropic mesh generation is completed, project the marked network nodes onto the matching geometric boundary, and reconstruct the matching boundary distribution based on the projection.

[0068] Optionally, step 42 includes:

[0069] Establish a hierarchical data structure between Part, Edge, Face, Connector, and Domain. Bind the geometry to the grid line, the geometry to the grid face, and the grid generation parameters to the part to enable the generation of anisotropic meshes for any specified part.

[0070] Optionally, see Figure 4 The method for generating anisotropic meshes by specifying arbitrary components includes:

[0071] Start mesh generation, traverse all parts, determine whether the current part has boundary layer mesh generation enabled, if boundary layer mesh generation is enabled, read the boundary layer parameter BoundaryLayerParams, obtain the associated geometric boundary GeomBoundary, start from the boundary, apply the boundary layer generation parameters to advance the generated network, check for early stopping conditions, until the anisotropic mesh generation ends; the parameters include the first layer height, the number of layers, and the growth rate.

[0072] This application also provides an embodiment of an adaptive height anisotropic mesh generation system, implementing the adaptive height anisotropic mesh generation method described in the above embodiment, comprising:

[0073] The initialization module is used to initialize the surface data of an object; the surface is the boundary line segment of the object in two dimensions, and the triangular or quadrilateral surface mesh of the object in three dimensions; the object is a two-dimensional / three-dimensional geometric entity that includes multiple parts; the parts of the object include the fuselage, wings, and engines of the passenger aircraft;

[0074] The first judgment module is used to determine whether there is a pushable array in the array data. If there is a pushable array, the normal of the array is calculated. Based on the normal of the array, the push direction of the array node is calculated. The Laplace smoothing algorithm can be used to iteratively optimize the push direction of the array node to obtain the push direction of the array node. The push step size of each array node is calculated. Based on the push direction and push step size of the array node, anisotropic elements are generated by pushing the array one by one.

[0075] The second judgment module is used to determine whether the generated anisotropic elements meet the early stopping condition. If the early stopping condition is met, the array data is updated. The early stopping condition includes geometric early stopping and proximity condition early stopping.

[0076] The mesh generation module is used to repeatedly run the first judgment module and the second judgment module until there are no more advanceable surfaces; all non-advanceable surfaces are used as the initial boundary for isotropic mesh generation, and isotropic meshes for the remaining space are generated using the isotropic mesh generation method.

[0077] This application also provides an embodiment of an electronic device, including a memory, a processor, and a computer program stored in the memory and executed by the processor, wherein the processor executes the computer program to implement the adaptive height anisotropic mesh generation method described in the above embodiments.

[0078] This application also provides an embodiment of a non-transitory computer-readable storage medium storing computer instructions for causing a computer to execute the adaptive height anisotropic mesh generation method described in the above embodiment.

[0079] The method described in the embodiments of this application was tested on two-dimensional and three-dimensional test cases. In two-dimensional testing, a single-segment airfoil and a three-segment airfoil were used as test cases, and in three-dimensional testing, a passenger aircraft was used. The generated height-adaptive, boundary-matched anisotropic meshes are shown below. Figures 6(a) to 6(d) As shown, the mesh smoothly transitions from anisotropic to isotropic, ensuring high mesh quality.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A method for generating anisotropic meshes with adaptive height, characterized in that, include: Step 1: Initialize the object's surface data; In two dimensions, the array surface is the boundary line segment of the object; in three dimensions, it is the triangular or quadrilateral mesh of the object. An object is a two-dimensional / three-dimensional geometric entity that includes multiple components; the components of an object include the fuselage, wings, and engines of a passenger aircraft. Step 2: Determine whether there are advanceable arrays in the array data. If there are advanceable arrays, calculate the normal of the array. Based on the normal of the array, calculate the advance direction of the array node. Iteratively optimize the advance direction of the array node to obtain the advance direction of the array node. Calculate the advance step size of each array node. Based on the advance direction and advance step size of the array node, advance the array one by one to generate anisotropic elements. Step 3: Determine whether the generated anisotropic elements meet the early stopping condition. If the early stopping condition is met, update the array data. The early stopping condition includes geometric early stopping and proximity condition early stopping. Step 4: Repeat steps 2 to 3 until there are no more advanceable surfaces; use all non-advanceable surfaces as the initial boundary for isotropic mesh generation, and use the isotropic mesh generation method to generate the isotropic mesh for the remaining space; The step of using all non-advanceable front surfaces as the initial boundary for isotropic mesh generation, and generating the isotropic mesh for the remaining space using an isotropic mesh generation method, includes: Step 41: Use the specified geometric boundary as the initial front surface for advancement to generate anisotropic meshes at the specified geometric boundary; Step 42: Match the nodes of the anisotropic mesh output in Step 41 with other boundaries: Set the boundary flag to be enabled in the component parameters, mark the mesh line connector or mesh surface domain to generate the anisotropic mesh, and mark the mesh line connector or mesh surface domain to be matched with the boundary layer; the component to be matched needs to enable boundary matching in the component parameters. Step 43: Perform node matching using either the pre-discrete matching method or the projection reconstruction matching method. Pre-discrete matching method: Based on the boundary layer generation parameters for matching, re-discrete the geometric lines bound to the mesh line Connector or mesh surface Domain to form new mesh lines or mesh surfaces that replace the original mesh lines or mesh surfaces and use them as the initial boundary surface to advance the generation of anisotropic meshes. Parameters include the first layer height, growth rate, and number of layers. Projection reconstruction matching method: Advance the generation of anisotropic meshes, marking the nodes that need to be matched during the generation process. After the anisotropic mesh generation is complete, project the marked network nodes onto the matching geometric boundary, and reconstruct the matching boundary distribution based on the projection.

2. The method for generating anisotropic meshes with adaptive height according to claim 1, characterized in that, In step 2, in the two-dimensional case, the front surface node is the endpoint of a line segment, and in the three-dimensional case, the front surface node is the vertex of a triangular or quadrilateral mesh. The front surface node has physical coordinates, which correspond to discrete calculation points in the flow field solver. The propulsion direction is a spatial vector used to control the mesh growth direction.

3. The method for generating anisotropic meshes with adaptive height according to claim 1, characterized in that, Step 3 also includes: If the generated anisotropic elements meet the early stopping condition, the current array surface stops early and will no longer be used to advance the generation of anisotropic meshes. Steps 2 to 3 are repeated until there are no more array surfaces to advance.

4. The method for generating anisotropic meshes with adaptive height according to claim 1, characterized in that, In step 3, geometric early stopping is related to the quality of the new cell, the current layer number, the cell size, and the cell aspect ratio; proximity condition early stopping is related to the set safety distance and the candidate array search range; both the safety distance and the candidate array search range are related to the advance step size.

5. The method for generating anisotropic meshes with adaptive height according to claim 1, characterized in that, Step 42 includes: Establish a hierarchical data structure between Part, Edge, Face, Connector, and Domain. Bind the geometry to the grid line, the geometry to the grid face, and the grid generation parameters to the part to enable the generation of anisotropic meshes for any specified part.

6. The method for generating anisotropic meshes with adaptive height according to claim 5, characterized in that, The method for generating anisotropic meshes by specifying arbitrary components includes: Start mesh generation, traverse all parts, determine whether the current part has boundary layer mesh generation enabled, if boundary layer mesh generation is enabled, read the boundary layer parameter BoundaryLayerParams, obtain the associated geometric boundary GeomBoundary, start from the boundary, apply the boundary layer generation parameters to advance the generated network, check for early stopping conditions, until the anisotropic mesh generation ends; the parameters include the first layer height, the number of layers, and the growth rate.

7. An adaptive height anisotropic mesh generation system, implementing the adaptive height anisotropic mesh generation method according to any one of claims 1-6, characterized in that, include: The initialization module is used to initialize the surface data of the object; In two dimensions, the array surface is the boundary line segment of the object; in three dimensions, it is the triangular or quadrilateral mesh of the object. An object is a two-dimensional / three-dimensional geometric entity that includes multiple components; the components of an object include the fuselage, wings, and engines of a passenger aircraft. The first judgment module is used to determine whether there is a pushable array in the array data. If there is a pushable array, the normal of the array is calculated. Based on the normal of the array, the push direction of the array node is calculated. The push direction of the array node is iteratively optimized to obtain the push direction of the array node. The push step size of each array node is calculated. Based on the push direction and push step size of the array node, anisotropic elements are generated by pushing the array one by one. The second judgment module is used to determine whether the generated anisotropic elements meet the early stopping condition. If the early stopping condition is met, the array data is updated. The early stopping condition includes geometric early stopping and proximity condition early stopping. The grid cell generation module is used to repeatedly run the first judgment module and the second judgment module until there are no more advanceable fronts. All non-advanceable front surfaces are used as the initial boundaries for isotropic mesh generation, and isotropic meshes for the remaining space are generated using isotropic mesh generation methods.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executed by the processor, characterized in that, When the processor executes the computer program, it implements the adaptive height anisotropic mesh generation method as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing a computer to execute the adaptive height anisotropic mesh generation method according to any one of claims 1 to 6.

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