A fully automatic volume mesh generation method based on structured surface meshes

Abstract

The present invention discloses a fully automatic volume mesh generation method based on structured surface meshes, which relates to the technical field of structured mesh generation, and comprises the following steps: generating pure docked multi-block structured surface meshes; generating structured body-fitting meshes based on multi-block structured surface meshes by using hyperbolic differential equations; assembling overlapping meshes based on structured body-fitting meshes to complete fully automatic volume mesh generation based on structured surface meshes. The present invention solves the problem that conventional mesh generation methods cannot guarantee the successful assembly of meshes and perform effective calculations.

Description

Technical Field

[0001] The invention relates to the technical field of structured grid generation, and in particular to a fully automatic volume grid generation method based on structured surface grids. Background Art

[0002] Structured grids have been widely used in applications with high accuracy requirements such as turbomachinery, wing airfoils, and aircraft due to their simple topology, simple and efficient memory indexing, and mature computing formats. In addition, since high-order algorithms in structured grids are more mature and efficient, and have better adaptability to GPU acceleration, structured grids have gradually received more and more attention in recent years.

[0003] In view of the difficulty of generating structured grids, overlapping grid technology can be used to solve the problem. For structured grids, overlapping grids can simplify the processing method of complex geometry. The complex geometry is decomposed into several parts with simple shapes, and structured grids are generated separately, and then the overlapping grids are assembled. This eliminates the topological constraints between grid parts and reduces the difficulty of grid generation while ensuring the quality of the grid.

[0004] However, in terms of grid generation, conventional overlay grid technology still cannot guarantee the successful assembly of grids or effective calculations, and requires repeated manual adjustments. This is specifically manifested in the following two points:

[0005] (1) The numerical format in structured grids requires that the grid is smooth enough, and corners and sudden changes in spacing should be avoided. Therefore, in sharp edges and corners, the generation of grids often requires manual slicing. For some corners, although they are common in practical applications, they are not a reliable grid for high-order calculations.

[0006] (2) In order to handle complex surfaces, the overlapping grid technique uses surface overlapping. This processing brings some additional difficulties. For example, special processing is required when integrating the surface aerodynamic force, and different grids have different approximations for curved walls, which leads to errors in the search for contributing units and requires special position corrections. These problems lead to the complexity of the overlapping grid technique. Summary of the invention

[0007] In view of the above-mentioned deficiencies in the prior art, the present invention provides a fully automatic volume mesh generation method based on structured surface meshes, which solves the problem that conventional mesh generation methods cannot guarantee successful mesh assembly and effective calculation.

[0008] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a fully automatic volume mesh generation method based on structured surface mesh, comprising the following steps:

[0009] S1: Generate pure docking multi-block structured surface mesh;

[0010] S2: Based on multi-block structured surface grids, structured body-fitting grid generation is performed using hyperbolic differential equations;

[0011] S3: Based on the structured body-fitted grid, overlapping grid assembly is performed to complete the fully automatic volume grid generation based on the structured surface grid.

[0012] The beneficial effect of the above scheme is that the present invention generates body-fitting meshes by partitioning multiple structured surface meshes that are purely docked, and assembles overlapping meshes. In the process of body mesh generation, since point-to-point connection is not required, the topological constraints between mesh components are eliminated, thereby greatly reducing the difficulty of mesh generation. At the same time, the mesh quality of each component can be independently controlled to form a high-quality structured mesh in the end. During the calculation process, each mesh component achieves full-field coupling in the overlapping area by interpolation. This technology provides a reasonable solution for high-precision numerical simulation of complex geometric structured meshes, solving the problem that conventional mesh generation methods cannot guarantee the successful assembly or effective calculation of meshes, and require repeated manual adjustments.

[0013] Furthermore, the S1 includes the following sub-steps:

[0014] S1-1: Establish the topological relationship of the surface of three-dimensional objects;

[0015] S1-2: Divide the three-dimensional surface into blocks according to the topological relationship of the three-dimensional surface, and determine the characteristic faces and characteristic edges;

[0016] S1-3: Generate mesh nodes on the feature edges to complete the generation of pure docking multi-block structured surface meshes.

[0017] The beneficial effect of the above further solution is that: through the above technical solution, the surface grid overlapping strategy is abandoned, and a purely docked multi-block structured surface grid is adopted to avoid the additional complexity of the contribution unit search and aerodynamic force integration.

[0018] Furthermore, S2 includes the following sub-steps:

[0019] S2-1: partition the object into convex corner areas and concave corner areas according to its shape;

[0020] S2-2: The multi-block structured surface meshes generated in each region are used as the initial state of mesh advancement generation. According to the density distribution of the generated meshes and the total advancement distance, the first-layer mesh spacing, mesh growth rate and advancement steps are specified;

[0021] S2-3: Based on the first-layer grid spacing, grid growth rate and advancement steps, set the real boundary conditions according to the boundary characteristics of the grid to be generated, and control the grid growth direction;

[0022] S2-4: Based on the grid growth direction, the hyperbolic equation is solved in each region according to the set grid generation parameters, the node coordinates of each layer of grid are calculated, the three-dimensional space grid is generated, and the generation of the structured body-fitting grid is completed.

[0023] The beneficial effect of the above further scheme is: in the conventional method, when generating a mesh for a convex or concave corner position, it is manifested that legal units cannot be extrapolated from certain local geometries. Therefore, the present invention partitions and extrapolates the surface and partitions it at the corner position to determine the boundaries of the partitions.

[0024] Furthermore, in S2-3, the real boundary conditions are set according to the boundary characteristics of the grid to be generated, and the grid growth direction is controlled, which specifically includes:

[0025] For the convex corner area, the normal direction of the object surface is used as the direction of mesh growth, and edge mesh blocks are added in the area where the mesh is missing to ensure that the mesh area overlaps;

[0026] For the concave angle region, when the concave angle is an acute angle, the grid generation directions on both sides are determined according to the concave angle; when the concave angle is an obtuse angle, the normal direction of the object surface is used as the direction of grid growth.

[0027] The beneficial effects of the above further scheme are: the present invention supplements edge grid blocks at convex corners to ensure grid area overlap; at concave corners, the propulsion direction of the surface grid is adjusted according to the concave angle to avoid the body grid on one side penetrating the surface of the object on the other side.

[0028] Furthermore, when the concave angle is an acute angle, the grid generation direction on both sides is determined according to the concave angle, specifically: the real boundary condition is determined by the boundary expected by the grid being generated, and the boundary condition is inclined outward at a fixed angle. On the boundary of :

[0029]

[0030]

[0031] in, is the increment of the position vector, is a constant, is a point on the boundary, is the position increment in three directions, For the The position vector of the step, For the The position vector of the step, superscript Represents the transpose of a matrix.

[0032] Furthermore, when the outer convex corner area and the inner concave corner are obtuse angles, the normal direction of the object surface is used as the direction of mesh growth, specifically: the boundary condition of mesh generation is set to a free boundary, and the formula is:

[0033]

[0034]

[0035] in, is the increment of the position vector, is a point on the boundary, is the extrapolation factor.

[0036] Furthermore, in S2-4, the hyperbolic equation is solved in each region according to the set grid generation parameters, the node coordinates of each layer of grid are calculated, and the calculation formula for generating the three-dimensional space grid is:

[0037] The control equations generated by the three-dimensional hyperbolic internal field grid are locally linearized about the known 0 state, and the formula is:

[0038]

[0039]

[0040]

[0041] in, is the position vector right The derivative of is the known state 0 position vector right The derivative of is the position vector right The derivative of is the known state 0 position vector right The derivative of is the position vector right The derivative of is the known state 0 position vector right The derivative of is the local grid cell volume, is the local grid cell volume at known state 0, , and They are the three directions of the space curve coordinate system;

[0042] exist and The finite difference method is used for numerical discretization in the direction, and the numerical dissipation term is added to obtain the algebraic equation of the discretized three-dimensional space grid:

[0043]

[0044]

[0045]

[0046]

[0047] in, is the identity matrix, and They are and Kinsey-Barth coefficient in direction, , and Respectively The coefficient matrix of the step, and They are and The difference operator in the direction, for The central difference operator of the Laplace operator in the direction, for The central difference operator of the Laplace operator in the direction, For the The position vector of the step, For the The position vector of the step, and They are and The dissipation coefficient in the direction, , , for The matrix of order, is the coordinate point in the rectangular coordinate system , and right The derivative of is the coordinate point in the rectangular coordinate system , and right The derivative of is the coordinate point in the rectangular coordinate system , and right The derivative of .

[0048] Furthermore, S3 includes the following sub-steps:

[0049] S3-1: Cut holes in the grids of the overlapping area and obtain the interpolation interface;

[0050] S3-2: Search for contributing units of the interpolation interface in the opposite and same side grids to complete overlapping grid assembly.

[0051] The beneficial effect of the above further scheme is: when assembling overlapping grids, if conventional overlapping grid assembly is used, the two overlapping grids need to invade each other's area deeply enough to form an overlapping area of ​​considerable width, which makes the overlapping grid assembly requirements higher and cannot be guaranteed to be successful in one go. Therefore, the present invention adopts polygonal interpolation based on face elements to reduce the requirements for the width of the overlapping area. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Flowchart of a fully automatic volume mesh generation method based on structured surface meshes.

[0053] Figure 2 This is a diagram of the structure of a purely docked multi-block structured surface grid.

[0054] Figure 3 Schematic diagram of overlapping grids at the outer convex corners.

[0055] Figure 4 Schematic diagram of overlapping grids when the concave edges are obtuse angles.

[0056] Figure 5 Schematic diagram of overlapping grids when the concave corners are acute.

[0057] Figure 6 Schematic diagram of bilateral flux interpolation in two dimensions. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0059] like Figure 1 As shown, a fully automatic volume mesh generation method based on structured surface meshes includes the following steps:

[0060] S1: Generate pure docking multi-block structured surface mesh;

[0061] S2: Based on multi-block structured surface grids, structured body-fitting grid generation is performed using hyperbolic differential equations;

[0062] S3: Based on the structured body-fitted grid, overlapping grid assembly is performed to complete the fully automatic volume grid generation based on the structured surface grid.

[0063] The pure docking multi-block structured surface in S1 refers to the mesh surfaces having common mesh nodes on the boundary edges, and they are point-to-point docked. However, the existing multi-block structured surface mesh refers to the mesh surfaces not being point-to-point docked on the boundary edges, but having overlapping.

[0064] The S1 includes the following sub-steps:

[0065] S1-1: Establish the topological relationship of the surface of three-dimensional objects;

[0066] In this embodiment, firstly, the CAD outputs an STL format file as a geometry file, then the three vertices of the triangular face are numbered counterclockwise, and then the angle between each triangular face and its adjacent triangular face is calculated;

[0067] S1-2: Divide the three-dimensional surface into blocks according to the topological relationship of the three-dimensional surface, and determine the characteristic faces and characteristic edges;

[0068] In this embodiment, the triangular facets are first grouped according to the angles between them to identify the characteristic faces, and then the boundary of each characteristic face is searched, and the common boundaries between the characteristic faces constitute characteristic edges;

[0069] S1-3: Generate mesh nodes on the feature edges to complete the generation of pure docking multi-block structured surface meshes, such as Figure 2 As shown;

[0070] Generate mesh nodes on feature edges. The specific method is:

[0071] S1-3-1: Use the space curve formula to describe each characteristic edge, with arc length The parametric equation of the space curve with parameter is:

[0072]

[0073] S1-3-2: Specify the number of mesh nodes on each feature edge;

[0074] S1-3-3: Discretize the space curve according to the number of grid nodes to obtain the arc length of each small segment of the curve , substituting into the space curve parameter equation, the coordinates of each grid node on the feature edge can be obtained.

[0075] The S2 includes the following sub-steps:

[0076] S2-1: partition the object into convex corner areas and concave corner areas according to its shape;

[0077] S2-2: The multi-block structured surface meshes generated in each region are used as the initial state of mesh advancement generation. According to the density distribution of the generated meshes and the total advancement distance, the first-layer mesh spacing, mesh growth rate and advancement steps are specified;

[0078] The specific implementation process is as follows: the pure docking multi-block structured surface meshes generated in each area are used as meshes to advance and generate the initial mesh surface. The coordinates of all mesh nodes on the initial mesh surface are known. The coordinates of a new layer of mesh points are advanced along the normal direction from the known layer of mesh points. The advancement method is to solve the hyperbolic equation, and the advancement distance is artificially given. After obtaining the coordinates of the new layer of mesh points, it is used as a known layer, and the above operation is repeated to obtain the coordinates of the next layer of mesh points, and the coordinates of all layers of mesh points are obtained by analogy;

[0079] The first layer grid spacing is the distance from the initial layer 0 to the first layer. h 0, which is given by humans. The grid growth rate is r For the k +1 level and k The ratio of layer advancement distance r = h k+1 / h k , then k Layer advancement distance h k = h 0* r k , the total number of grid advancement steps is N. Therefore, if you specify h 0、 r and N, the total distance for overall mesh generation and computational mesh advancement;

[0080] S2-3: Based on the first-layer grid spacing, grid growth rate and advancement steps, set the real boundary conditions according to the boundary characteristics of the grid to be generated, and control the grid growth direction;

[0081] S2-4: Based on the grid growth direction, the hyperbolic equation is solved in each region according to the set grid generation parameters, the node coordinates of each layer of grid are calculated, the three-dimensional space grid is generated, and the generation of the structured body-fitting grid is completed.

[0082] In one embodiment of the present invention, if the shape of the surface of an object is relatively complex, it is difficult to obtain a body-fitting mesh by extrapolating the surface mesh as a whole. For example, it is difficult to coordinate when generating meshes at convex or concave corners, which is specifically manifested in that it is impossible to extrapolate legal units from certain local geometries. For these special cases, the specific solutions are as follows:

[0083] The surface is partitioned and extrapolated, and the partitions are made at the corners to determine the boundaries of the partitions. Figure 3 As shown in , for convex corners, due to the partition extrapolation, there will be grid missing in the area above the grid source point. At this time, the edge grid blocks are added in this area to ensure the grid area overlap. For concave corners, such as Figure 4 and Figure 5 As shown in the figure, at this time, the advancing direction of the surface mesh needs to be adjusted according to the concave angle to avoid the body mesh on one side penetrating the surface of the object on the other side.

[0084] In S2-3, the real boundary conditions are set according to the boundary characteristics of the grid to be generated, and the grid growth direction is controlled, which specifically includes:

[0085] For the convex corner area, the normal direction of the object surface is used as the direction of mesh growth, and edge mesh blocks are added in the area where the mesh is missing to ensure that the mesh area overlaps;

[0086] For the concave angle area, when the concave angle is an acute angle, in order to avoid the body mesh on one side penetrating the object surface on the other side and to ensure that the generated meshes have sufficient overlap, the mesh generation directions on both sides are determined according to the concave angle; when the concave angle is an obtuse angle, the object surface normal is used as the mesh growth direction.

[0087] When the concave angle is acute, such as Figure 5 As shown, the side boundary is inclined outward at a fixed angle. This boundary condition can be implemented using an implicit boundary, specifically by making the dependent variable exist i =1 on the boundary that satisfies the following conditions:

[0088]

[0089] in, is the increment of the position vector, is a constant, is a point on the boundary, is the position increment in three directions, For the The position vector of the step, For the The position vector of the step, superscript Represents the transpose of a matrix.

[0090] In this case, starting from the initial surface, the direction of the first layer boundary mesh growth needs to be smaller than the concave angle.

[0091] At the obtuse angle of the inner concave and the outer convex corner, the normal direction of the object surface is used as the direction of mesh growth, and the edge mesh blocks are supplemented in the area where the mesh of the outer convex corner is missing to ensure the overlap of the mesh area. In these two cases, there are no specific restrictions on the mesh of the boundary surface, and the boundary condition of the mesh generation can be set to a free boundary. Specifically: Set the boundary condition of the mesh generation to a free boundary, the formula is:

[0092]

[0093]

[0094] in, is the extrapolation factor, if Free floating conditions can be achieved; if , the boundary can be tilted outward away from the inner field grid.

[0095] In S2-4, the hyperbolic equation is solved in each region according to the set grid generation parameters, the node coordinates of each layer of grid are calculated, and the calculation formula for generating the three-dimensional space grid is:

[0096] The control equations generated by the three-dimensional hyperbolic internal field grid are locally linearized about the known 0 state, and the formula is:

[0097]

[0098]

[0099]

[0100] in, is the position vector right The derivative of is the known state 0 position vector right The derivative of is the position vector right The derivative of is the known state 0 position vector right The derivative of is the position vector right The derivative of is the known state 0 position vector right The derivative of is the local grid cell volume, is the local grid cell volume at known state 0, , and They are the three directions of the space curve coordinate system;

[0101] Coordinate points in the curvilinear coordinate system ( ξ , η , ζ ) and the coordinate point in the rectangular coordinate system ( x , y , z ) There is a one-to-one correspondence relationship;

[0102]

[0103] exist and The finite difference method is used for numerical discretization in the direction, and the numerical dissipation term is added to obtain the algebraic equation of the discretized three-dimensional space grid:

[0104]

[0105]

[0106]

[0107]

[0108] in, is the identity matrix, and They are and Kinsey-Barth coefficient in direction, , and Respectively The coefficient matrix of the step, and They are and The difference operator in the direction, for The central difference operator of the Laplace operator in the direction, for The central difference operator of the Laplace operator in the direction, For the The position vector of the step, For the The position vector of the step, and They are and The dissipation coefficient in the direction, , , for The matrix of order, , For the The local grid cell volume of the step, superscript represents the transpose of a matrix, is the coordinate point in the rectangular coordinate system , and right The derivative of is the coordinate point in the rectangular coordinate system , and right The derivative of is the coordinate point in the rectangular coordinate system , and right The derivative of .

[0109] The S3 includes the following sub-steps:

[0110] S3-1: Cut holes in the grids of the overlapping area and obtain the interpolation interface;

[0111] S3-2: Search for contributing units of the interpolation interface in the opposite and same side grids to complete overlapping grid assembly.

[0112] In this embodiment, if there are multiple sets of grids in the same area, this area is an overlapping area. In the overlapping grid area, for one set of grids A, the edges of its outermost grid cells are interpolation interfaces, and the edges of these cells can be marked when cutting holes, and the same operation is performed on other grids.

[0113] For the interpolation interface marked by mesh A in the hole cutting, the nearest mesh cells in mesh B are searched in the overlapping area. These cells are the contributing cells, and the edges of these cells are the contributing interfaces. The contributing cells and the contributing interfaces constitute the interpolation template of the interpolation interface on mesh A. The above process is overlapping mesh assembly.

[0114] like Figure 6 As shown, in the traditional overlapping grid, the interpolation unit is a multi-layer interpolation unit, and the present invention uses the boundary surface element of the grid A as the interpolation interface. If the interpolation accuracy needs to be improved, the units and interfaces on both sides of the interpolation interface can be used as contributing units and interfaces. For the selection of the interpolation method, the least squares can be used with ENO or WENO to ensure the accuracy requirements and discontinuous capture.

[0115] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the invention.

Claims

1. A fully automatic volume mesh generation method based on structured surface meshes, characterized in that: The following steps are involved: S1: Generate multi-block structured surface meshes for pure docking of aircraft; S2: Based on multi-block structured surface grids, hyperbolic differential equations are used to generate structured body-fitted grids for aircraft; S3: Based on the structured body-fitted grid of the aircraft, the aircraft overlapping grid is assembled to complete the fully automatic volume grid generation based on the structured surface grid; The S1 includes the following sub-steps: S1-1: Establish the topological relationship of the surface of three-dimensional objects; S1-2: Divide the surface of the three-dimensional object into blocks according to the topological relationship of the surface of the three-dimensional object, and determine the characteristic faces and characteristic edges; S1-3: Generate mesh nodes on the feature edges to complete the generation of multi-block structured surface meshes for pure docking of the aircraft; The S2 includes the following sub-steps: S2-1: partition the object into convex corner areas and concave corner areas according to its shape; S2-2: The multi-block structured surface meshes generated in each region are used as the initial state of mesh advancement generation. According to the density distribution of the generated meshes and the total advancement distance, the first-layer mesh spacing, mesh growth rate and advancement steps are specified; S2-3: Based on the first-layer grid spacing, grid growth rate and advancement steps, set the real boundary conditions according to the boundary characteristics of the grid to be generated, and control the grid growth direction; In S2-3, the real boundary conditions are set according to the boundary characteristics of the grid to be generated, and the grid growth direction is controlled, which specifically includes: For the convex corner area, the normal direction of the object surface is used as the direction of mesh growth, and edge mesh blocks are added in the area where the mesh is missing to ensure that the mesh area overlaps; For the concave angle region, when the concave angle is an acute angle, the grid generation directions on both sides are determined according to the concave angle; when the concave angle is an obtuse angle, the normal direction of the object surface is used as the grid growth direction; When the concave angle is an acute angle, the grid generation direction on both sides is determined according to the concave angle, specifically: the real boundary condition is determined by the boundary expected by the grid being generated, and the boundary condition is inclined outward at a fixed angle. On the boundary of : in, is the increment of the position vector, is a constant, is a point on the boundary, is the position increment in three directions, For the The position vector of the step, For the The position vector of the step, superscript Represents the transpose of a matrix; When the outer convex corner area and the inner concave corner are obtuse angles, the normal direction of the object surface is used as the direction of mesh growth. Specifically, the boundary condition of mesh generation is set to a free boundary, and the formula is: in, is the increment of the position vector, is a point on the boundary, is the extrapolation factor; S2-4: Based on the grid growth direction, the hyperbolic equation is solved in each region according to the set grid generation parameters, the node coordinates of each layer of grid are calculated, and the three-dimensional space grid is generated to complete the generation of the structured body-fitting grid of the aircraft; The S3 includes the following sub-steps: S3-1: Cut holes in the grids of the overlapping area and obtain the interpolation interface; S3-2: Search for the contributing units of the interpolation interface in the opposite and same side grids to complete the overlapping grid assembly of the aircraft.

2. The method for generating a fully automatic volume mesh based on a structured surface mesh according to claim 1, characterized in that: In S2-4, the hyperbolic equation is solved in each region according to the set grid generation parameters, the node coordinates of each layer of grid are calculated, and the calculation formula for generating the three-dimensional space grid is: The control equations generated by the three-dimensional hyperbolic internal field grid are locally linearized about the known 0 state, and the formula is: in, is the position vector right The derivative of is the known state 0 position vector right The derivative of is the position vector right The derivative of is the known state 0 position vector right The derivative of is the position vector right The derivative of is the known state 0 position vector right The derivative of is the local grid cell volume, is the local grid cell volume at known state 0, , and They are the three directions of the space curve coordinate system; exist and The finite difference method is used for numerical discretization in the direction, and the numerical dissipation term is added to obtain the algebraic equation of the discretized three-dimensional space grid: in, is the identity matrix, and They are and Kinsey-Barth coefficient in direction, , and Respectively The coefficient matrix of the step, and They are and The difference operator in the direction, for The central difference operator of the Laplace operator in the direction, for The central difference operator of the Laplace operator in the direction, For the The position vector of the step, For the The position vector of the step, and They are and The dissipation coefficient in the direction, , , for The matrix of order, is the coordinate point in the rectangular coordinate system , and right The derivative of is the coordinate point in the rectangular coordinate system , and right The derivative of is the coordinate point in the rectangular coordinate system , and right The derivative of .

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