Curved surface grid generation and self-adaptive re-division method for fluid simulation

Abstract

The invention discloses a curved surface grid generation and self-adaptive re-division method for fluid simulation. The method comprises the following steps: acquiring CAD fluid model data; processing closed surface, short edge and parameter domain distortion and geometric interference problems of the CAD fluid model to obtain a defect-free continuous geometric model; performing curved surface discretization processing on the defect-free continuous geometric model to generate an initial grid; and performing grid re-division processing on the initial grid to generate an optimized anisotropic curved surface grid. The problems of high geometric defect sensitivity, large isotropic grid redundancy and sudden size change of the tail end of a parameter domain in related technologies of fluid simulation are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational fluid dynamics simulation, and in particular relates to a surface mesh generation and adaptive re-division method for fluid simulation. Background Art

[0002] Mesh generation is a core basic step in numerical simulation. Its quality directly determines the accuracy and convergence efficiency of downstream flow field solutions. It is also the key link with the most intensive manual intervention and the longest time in engineering practice. In the field of fluid simulation, the surface mesh of complex geometric models (such as aircraft engine blades and aircraft wing surfaces) must meet two stringent requirements: one is the high-fidelity discretization of geometric features, and the other is the efficient adaptation of flow anisotropic characteristics. However, traditional mesh generation methods face significant challenges in such scenarios.

[0003] Traditional methods lack the ability to effectively handle closed surfaces, short edges, and parameter domain distortion in geometric models. For example, since the parameter domain boundary ring of a closed surface is composed of only a single closed curve, if it is not divided into multiple parameter curves, it will lead to abnormal distribution of sampling points when the surface is discretized, causing non-manifold mesh errors; local geometric distortion caused by short edges will destroy the continuity of the parameter domain and cause a sudden change in mesh size; and parameter domain distortion (such as NURBS surface distortion) will cause the normal deviation of the physical space to exceed the standard, directly affecting the reliability of flow field calculations. In addition, the uniform grid generated by the existing method produces a large number of redundant units in the curvature mutation area (such as the leading edge of the blade and the wing joint), which significantly increases the consumption of computing resources, and cannot dynamically adjust the unit size along the main curvature direction, making it difficult to efficiently capture anisotropic flow characteristics such as shock boundary layer and detached vortex.

[0004] When the curve is discretized, if the residual of the short side at the end of the parameter domain is forcibly truncated, it will cause a sudden change in the mesh size, which will in turn cause numerical oscillations in the velocity and pressure gradient of the flow field, affecting the convergence of the simulation. For example, if the residual of the short side at the end of the discrete curve of the leading edge of the wing is not reasonably allocated, the mutation rate of the local mesh size may exceed the threshold, causing the flow field calculation to diverge.

[0005] Although traditional surface mesh generation methods can handle simple geometric models, they still have obvious shortcomings when facing the above problems: the mesh normal deviation in the parameter domain mapping distortion area is difficult to control, the redundant units in the curvature rapid change area cannot be adaptively optimized, and there is a lack of effective strategy for the residual allocation of the short edge at the end of the curve. Therefore, there is an urgent need for a surface mesh generation method that can automatically repair geometric defects, suppress size mutations, and adapt to anisotropic characteristics to improve the accuracy and efficiency of fluid simulation. Summary of the invention

[0006] The embodiment of the present application provides a surface mesh generation and adaptive re-division method for fluid simulation to solve the problems of high sensitivity to geometric defects, large redundancy of isotropic meshes, and sudden size changes at the end of the parameter domain existing in fluid simulation related technologies.

[0007] According to an embodiment of the present application, a surface mesh generation and adaptive re-division method for fluid simulation is provided, comprising: S1: Obtain CAD fluid model data; S2: Processing the closed surface, short edge, parameter domain distortion and geometric interference problems of the CAD fluid model to obtain a defect-free continuous geometric model; S3: performing surface discretization processing on the defect-free continuous geometric model to generate an initial mesh; S4: Re-meshing the initial mesh to generate an optimized anisotropic surface mesh.

[0008] Optionally, the CAD fluid model is processed for closed surfaces, short edges, parameter domain distortion and geometric interference problems to obtain a defect-free continuous geometric model, including: S21: performing closed surface detection on the CAD fluid model, and if a closed surface exists, segmenting its parameter domain and constructing related parameter curves to obtain a continuous geometric model without a closed surface; S22: performing short edge detection on the continuous geometric model without closed surfaces, and if there is a short edge whose length is less than a preset threshold, merging adjacent short edges to obtain a continuous geometric model without short edges; S23: performing parameter domain distortion detection on the continuous geometric model without short edges, and if there is a surface with parameter domain distortion, performing surface interpolation reconstruction to obtain a continuous geometric model without parameter domain distortion; S24: performing geometric interference detection on the continuous geometric model without parameter domain distortion, and if there is a geometric interference area, correcting the topological structure through Boolean operation, and finally generating a defect-free continuous geometric model.

[0009] Optionally, performing surface discretization processing on the defect-free continuous geometric model to generate an initial mesh includes: S31: performing boundary curve extraction processing on the defect-free continuous geometric model to obtain a boundary curve set of the surface; S32: performing adaptive curve discretization processing on the boundary curve set. If there is a problem of short ends when the curve is discretized, a smoothing algorithm is used to regard the short ends as residuals and evenly distribute them to other discrete curve segments to generate a discrete point set of the physical space boundary curve. S33: performing parameter domain mapping processing on the discrete point set of the physical space boundary curve to generate a discrete point set of the parameter space boundary curve; S34: constructing an initial bounding box based on the discrete point set of the parameter space boundary curve as a quadtree root node; S35: performing anisotropic subdivision processing on the root node of the quadtree, performing encryption operation based on the joint criterion of zero-order geometric deviation, first-order tangent tolerance, and second-order normal tolerance, and generating an anisotropic quadtree encryption lattice; S36: Based on the anisotropic quadtree encrypted point lattice and the parameter space boundary curve discrete point set, perform Delaunay triangulation processing with hole constraints to generate an initial surface mesh.

[0010] Optionally, re-meshing the initial mesh to generate an optimized anisotropic surface mesh includes: S41: performing low-quality short edge detection on the initial surface mesh, and if there is a short edge whose edge length is less than a length threshold and whose adjacent unit dihedral angle is greater than an angle threshold, performing edge-folding-based topology optimization to generate a topology optimized mesh; S42: performing local curvature gradient analysis on the topology optimized mesh, dynamically adjusting vertex distribution density according to a comparison result between a curvature gradient value and a density threshold, and generating a density optimized mesh; S43: Performing unit quality evaluation on the density optimized grid, if there are units with quality factors lower than the quality threshold, performing anisotropic local subdivision to generate an optimized anisotropic surface grid.

[0011] The technical solution provided by the present invention includes the following beneficial effects: The present invention converts defective input data into a defect-free continuous geometric model by processing the closed surface, short edge, parameter domain distortion and geometric interference problems of the original CAD fluid model, effectively avoiding mesh generation failures caused by geometric quality problems and improving the pre-processing robustness of complex fluid simulation. Based on anisotropic surface discretization and mesh repartitioning technology, the mesh density is dynamically adjusted along the characteristic gradient direction in the curvature mutation area to generate a high-resolution anisotropic surface mesh, which can not only accurately capture the flow field gradient characteristics, but also significantly reduce the number of redundant units and reduce computing resource consumption. This method automates the entire process from geometric repair to mesh output without relying on manual intervention, can efficiently adapt to the engineering simulation requirements of complex fluid shapes, and greatly shortens the simulation pre-processing cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0013] Figure 1 The present invention is a flow chart of a surface mesh generation and adaptive re-division method for fluid simulation, showing an embodiment.

[0014] Figure 2 The figure is a schematic diagram of the original geometric model of a passenger aircraft according to an embodiment.

[0015] Figure 3 It is a schematic diagram of the closed surface processing effect shown in an embodiment, showing the parameter domain segmentation process of the closed surface of the side of the cylindrical model.

[0016] Figure 4 It is a schematic diagram showing a comparison of wing-fuselage interference processing of a passenger aircraft according to an embodiment.

[0017] Figure 5 The figure is a schematic diagram of parameter domain projection and initial quadtree construction according to an embodiment.

[0018] Figure 6 The figure is a schematic diagram of Delaunay triangulation according to an embodiment.

[0019] Figure 7 An optimized anisotropic surface mesh is shown in an embodiment.

[0020] Figure 8 The figure is a schematic diagram showing the change of the drag coefficient and lift coefficient of the fuselage surface with the number of iterations according to an embodiment.

[0021] Fig. 9 The figure is a schematic diagram of the flow field distribution (static pressure, turbulent kinetic energy and velocity) in the cabin area of ​​a passenger aircraft according to an embodiment.

[0022] Fig.10 The figure is a schematic diagram of the flow field distribution (pressure, turbulent kinetic energy and velocity) in the wing root area of ​​a passenger aircraft according to an embodiment. DETAILED DESCRIPTION

[0023] The method of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0024] The present invention supports the efficient processing of complex CAD fluid models, which refer to three-dimensional geometric models constructed by CAD technology for fluid mechanics simulation. Typical applications include engineering objects such as passenger aircraft, aircraft engine blades, aircraft wing surfaces, and turbomachinery groups. Such models must meet strict geometric accuracy and topological integrity requirements to avoid mesh generation failure or flow field simulation distortion due to problems such as closed surfaces, short edges, or sudden changes in curvature. This method can directly process the original model with the above defects through geometric repair and anisotropic surface mesh generation, and output a high-fidelity surface mesh that strictly fits the geometric features to meet the needs of high-precision flow field solutions.

[0025] Figure 1 A surface mesh generation and adaptive re-division method for fluid simulation is shown as an embodiment. The method comprises the following steps: S1: Get CAD fluid model data: Specifically, the CAD fluid model data is parsed through the geometry engine Open CASCADE. Figure 2 The CAD model data of the passenger aircraft shown is an example, 145 boundary curves are extracted, and 54 geometric surfaces are parsed. Among them, the wing of the passenger aircraft is composed of 8 groups of NURBS surfaces, and the fuselage is spliced ​​by 12 groups of B-spline surfaces. During the parsing process, the geometric topological relationship between each component is completely preserved.

[0026] S2: Processing the closed surface, short edge, parameter domain distortion and geometric interference problems of the CAD fluid model to obtain a defect-free continuous geometric model; this step may include the following sub-steps: S21: performing closed surface detection on the CAD fluid model, and if a closed surface exists, segmenting its parameter domain and constructing related parameter curves to obtain a continuous geometric model without a closed surface; For the annular closed surface of the passenger aircraft engine nacelle (whose parameter domain is a single closed curve ring, logical and Figure 3 The cylindrical model shown in Figure 1 is consistent with the cylindrical model shown in Figure 1), which is first split into two symmetrical subintervals by the parameter domain segmentation algorithm: u=[0,0.5] and u=[0.5,1]. Here, the parameter u∈[0,1] represents the normalized curve parameter domain, where u=0 and u=1 coincide due to the closed property. Subsequently, the relevant new B-spline parametric curves are independently generated in each subinterval. This method significantly improves the uniformity of the parameter distribution of the inner and outer wall surfaces of the nacelle and eliminates the possible mesh distortion when the original closed surface is parameterized.

[0027] S22: performing short edge detection on the continuous geometric model without closed surfaces, and if there is a short edge whose length is less than a preset threshold, merging adjacent short edges to obtain a continuous geometric model without short edges; Specifically, short edges with lengths less than a threshold are detected at the connection between the winglet and the main wing of the passenger aircraft. The geometric discontinuity area is eliminated through vertex merging operations to generate a smooth transition surface and ensure the uniform distribution of subsequent mesh sizes at the connection.

[0028] S23: performing parameter domain distortion detection on the continuous geometric model without short edges, and if there is a surface with parameter domain distortion, performing surface interpolation reconstruction to obtain a continuous geometric model without parameter domain distortion; Specifically, the parameter domain of the aircraft wing surface was detected and it was found that the local surface parameter domain was distorted. The NURBS interpolation algorithm was used to recalculate the control point weights, and the reconstructed surface parameter domain was evenly distributed, restoring the linear mapping relationship between the physical domain and the parameter domain.

[0029] S24: performing geometric interference detection on the continuous geometric model without parameter domain distortion, and if a geometric interference area exists, correcting the topological structure through Boolean operation to generate the defect-free continuous geometric model; Specifically, for the geometric interference area between the wing and the fuselage of the passenger aircraft (such as Figure 4 As shown in the figure), Boolean operations are performed to trim the interlaced surfaces. After processing, a smooth transition topological structure is formed at the wing-fuselage connection, ensuring the physical rationality of subsequent mesh generation.

[0030] S3: performing surface discretization processing on the defect-free continuous geometric model to generate an initial mesh; this step may include the following sub-steps: S31: performing boundary curve extraction processing on the defect-free continuous geometric model to obtain a surface boundary curve set; Specifically, based on the "face-edge-vertex" topological hierarchy, all boundary curves associated with the surface are extracted. For example, the boundary curve set of the leading edge surface of a passenger aircraft wing includes the leading edge line, the wing root connection line and the wing tip transition line, which completely covers the geometric contour of the surface.

[0031] S32: performing adaptive curve discretization processing on the boundary curve set. If there is a problem of short ends when the curve is discretized, a smoothing algorithm is used to regard the short ends as residuals and evenly distribute them to other discrete curve segments to generate a discrete point set of the physical space boundary curve. Specifically, during the discretization of the NURBS curve of the leading edge of the wing of an aircraft, a short edge at the end appears, which is regarded as the residual And distribute them to the preceding discrete segments according to the size ratio. Update the node parameters as follows:

[0032] In the formula Represents the total number of discrete points, Represents the index of the current discrete point, represents the original node parameter value, Indicates the updated node parameter value, thereby eliminating the size mutation caused by traditional truncation and achieving a smooth transition of discrete node spacing.

[0033] S33: performing parameter domain mapping processing on the discrete point set of the physical space boundary curve to generate a discrete point set of the parameter space boundary curve; Specifically, the discrete points on the physical space boundary curve are projected into the parameter domain of the surface to be discretized to obtain a discrete point set of the parameter space boundary curve.

[0034] S34: constructing an initial bounding box based on the discrete point set of the parameter space boundary curve as a quadtree root node; Specifically, Figure 5As shown, the initial bounding box is constructed with the minimum circumscribed rectangle of the discrete points in the parameter space, and the bounding box is directly used as the root node of the quadtree.

[0035] S35: performing anisotropic subdivision processing on the root node of the quadtree, performing encryption operation based on the joint criterion of zero-order geometric deviation, first-order tangent tolerance, and second-order normal tolerance, and generating an anisotropic quadtree encryption lattice; Specifically, the zero-order geometric deviation criterion is defined, with the center point of the quadtree node For the test point, calculate the shortest distance from it to the original geometric surface , constraining the distance to not exceed the preset threshold. If the geometric deviation from the physical surface exceeds the limit, it is determined that the quadtree node needs to be subdivided; Specifically, the first-order tangent tolerance criterion is defined, with the center point of the quadtree node As a benchmark, calculate the maximum angle between the tangent vector of the four adjacent sub-node centers in the parameter direction. ,constraint Does not exceed the preset threshold. If the tangential change angle exceeds the limit, it is determined that the node needs to be subdivided along the parameter direction.

[0036] Specifically, define the second-order normal tolerance criterion, with the center point of the quadtree node As a benchmark, calculate the normal vector deviation angle between it and the center points of the four adjacent child nodes, and constrain the maximum deviation angle Does not exceed the preset threshold. If the normal deviation exceeds the limit, it is determined that the node needs to be subdivided along the normal sensitive direction.

[0037] S36: Based on the anisotropic quadtree encrypted point lattice and the parameter space boundary curve discrete point set, perform Delaunay triangulation processing with hole constraints to generate an initial surface mesh; Specifically, for the hole area of ​​the passenger aircraft fuselage (such as the connection with the wing), a constraint point set is generated in the parameter domain, and the Delaunay triangulation with hole constraints is performed by combining the anisotropic quadtree encrypted point lattice and the parameter space boundary curve discrete point set, such as Figure 6 This is a schematic diagram of Delaunay triangulation. The generated initial mesh strictly follows the geometric contour and meets the stability requirements of the CFD solver.

[0038] S4: re-meshing the initial mesh and outputting an optimized anisotropic surface mesh; this step may include the following sub-steps: S41: performing low-quality short edge detection on the initial surface mesh, and if there is a short edge whose edge length is less than a length threshold and whose adjacent unit dihedral angle is greater than an angle threshold, performing edge-folding-based topology optimization to generate a topology optimized mesh; Specifically, low-quality short edges in the initial mesh are detected at the tail of the passenger aircraft nacelle. When it is detected that the edge length is less than a length threshold and the adjacent unit dihedral angle is greater than an angle threshold, an edge collapse operation is performed to merge adjacent vertices.

[0039] S42: performing local curvature gradient analysis on the topology optimized mesh, dynamically adjusting vertex distribution density according to a comparison result between a curvature gradient value and a density threshold, and generating a density optimized mesh; Specifically, for the high curvature area of ​​the leading edge of the passenger aircraft wing, the local curvature gradient value is calculated. When the curvature gradient exceeds the density threshold, the vertex density is adjusted.

[0040] S43: performing unit quality evaluation on the density optimized grid, and if there are units whose quality factors are lower than the quality threshold, performing anisotropic local subdivision to generate an optimized anisotropic surface grid; Specifically, the quality factor of the mesh cells in the wing root area of ​​the passenger aircraft is evaluated. For cells with a quality factor below a threshold, the quality of the mesh cells is improved by inserting new nodes and topological transformation, such as Figure 7 As shown in the figure, the quality of the optimized passenger aircraft mesh meets the stability requirements of fluid simulation.

[0041] Taking the passenger aircraft model as an example, 30,272 anisotropic surface meshes and 472,564 volume meshes were generated by this method. Figure 8 (a) shows that the drag coefficient decreases monotonically with the increase of iteration number, and finally stabilizes within the fluctuation range of ±0.5%. Figure 8 (b) in the figure shows that the lift coefficient converges quickly in the early stage of iteration, and the fluctuation amplitude is less than 0.3% in the later stage, which verifies the computational stability of the grid generation process.

[0042] The static pressure distribution in the engine nacelle area is as follows: Fig. 9 As shown in (a), its gradient characteristics are highly consistent with the curvature change of the fluid shape, verifying the accurate mapping of the grid to the geometric features; Fig. 9 The turbulent kinetic energy distribution shown in (b) shows that there is no abnormal energy accumulation at the leading edge of the blade, and the energy dissipation trend conforms to the physical law; Fig. 9 The velocity vector diagram (c) in the figure accurately analyzes the three-dimensional vortex structure of the lip separation vortex, proving the ability of the grid to capture local flow details. Verification in the wing root area shows that: Fig.10 The pressure gradient distribution of the static pressure cloud diagram (a) is consistent with the theoretical prediction. Fig.10 (b) Turbulent kinetic energy and Fig.10 The velocity distributions in (c) all show boundary layer evolution characteristics that match high Reynolds number flows. The above multi-dimensional flow field characteristics verification results confirm that the grid generated by this method has the ability to analyze complex fluid phenomena with high fidelity.

[0043] It can be seen from the above technical solutions that the present invention has the following beneficial effects: Geometric defect repair capability: By dividing the parameter domain boundary ring of the closed surface into multiple parameter curves, merging the short edges, and reconstructing the parameter domain distortion surface, this method can eliminate the geometric defects of the input model and ensure the rationality of the sampling point distribution during the surface discretization process. Boolean operations effectively handle geometric interference areas and avoid the generation of non-manifold meshes, thereby providing topologically complete geometric input for subsequent flow field solutions.

[0044] Anisotropic feature adaptation: Based on the joint criteria of zero-order geometric deviation, first-order tangent tolerance and second-order normal tolerance, the quadtree nodes are driven to dynamically subdivide along the direction of the maximum feature transformation. This anisotropic encryption strategy significantly reduces redundant units in areas with sudden changes in curvature (such as the leading edge of the blade), while improving the grid resolution along the direction of maximum feature transformation to efficiently capture the gradient characteristics of the flow field. When short-side problems occur in curve discretization, the residual at the end of the parameter domain is weighted and distributed to the preceding discrete segment according to the size ratio, avoiding the size mutation problem caused by traditional forced truncation and ensuring a smooth transition of the grid size.

[0045] Optimization of mesh quality and computational efficiency: The Delaunay triangulation algorithm with hole constraints is combined with the winding number theory to accurately identify the topological relationship between the inner and outer rings, generate uniform constraint points within the inner ring bounding box, and effectively suppress mesh misjudgment in the hole area. The edge folding algorithm eliminates low-quality short edges, and dynamically adjusts the vertex density in combination with the local curvature gradient, significantly improving the aspect ratio and normal consistency of the unit. In the mesh re-division stage, local subdivision is performed on the isotropic units, which greatly reduces the proportion of units with quality factors below the set threshold, meeting the high-precision requirements of the CFD solver.

[0046] Those skilled in the art will readily appreciate other embodiments of the present application after considering the description and practicing the contents disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The description and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the claims.

[0047] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A surface mesh generation and adaptive re-meshing method for fluid simulation, characterized in that: include: S1: Obtain CAD fluid model data; S2: Processing the closed surface, short edge, parameter domain distortion and geometric interference problems of the CAD fluid model to obtain a defect-free continuous geometric model; S3: performing surface discretization processing on the defect-free continuous geometric model to generate an initial mesh; S4: Re-meshing the initial mesh to generate an optimized anisotropic surface mesh.

2. The method according to claim 1, characterized in that: The CAD fluid model is processed for closed surfaces, short edges, parameter domain distortion and geometric interference problems to obtain a defect-free continuous geometric model, including: S21: performing closed surface detection on the CAD fluid model, and if a closed surface exists, segmenting its parameter domain and constructing related parameter curves to obtain a continuous geometric model without a closed surface; S22: performing short edge detection on the continuous geometric model without closed surfaces, and if there is a short edge whose length is less than a preset threshold, merging adjacent short edges to obtain a continuous geometric model without short edges; S23: performing parameter domain distortion detection on the continuous geometric model without short edges, and if there is a surface with parameter domain distortion, performing surface interpolation reconstruction to obtain a continuous geometric model without parameter domain distortion; S24: performing geometric interference detection on the continuous geometric model without parameter domain distortion, and if there is a geometric interference area, correcting the topological structure through Boolean operation, and finally generating a defect-free continuous geometric model.

3. The method according to claim 1, characterized in that The defect-free continuous geometric model is subjected to surface discretization processing to generate an initial mesh, including: S31: performing boundary curve extraction processing on the defect-free continuous geometric model to obtain a boundary curve set of the surface; S32: performing adaptive curve discretization processing on the boundary curve set. If there is a problem of short ends when the curve is discretized, a smoothing algorithm is used to regard the short ends as residuals and evenly distribute them to other discrete curve segments to generate a discrete point set of the physical space boundary curve. S33: performing parameter domain mapping processing on the discrete point set of the physical space boundary curve to generate a discrete point set of the parameter space boundary curve; S34: constructing an initial bounding box based on the discrete point set of the parameter space boundary curve as a quadtree root node; S35: performing anisotropic subdivision processing on the root node of the quadtree, performing encryption operation based on the joint criterion of zero-order geometric deviation, first-order tangent tolerance, and second-order normal tolerance, and generating an anisotropic quadtree encryption lattice; S36: Based on the anisotropic quadtree encrypted point lattice and the parameter space boundary curve discrete point set, perform Delaunay triangulation processing with hole constraints to generate an initial surface mesh.

4. The method according to claim 1, characterized in that: The initial mesh is re-meshed to generate an optimized anisotropic surface mesh, including: S41: performing low-quality short edge detection on the initial surface mesh, and if there is a short edge whose edge length is less than a length threshold and whose adjacent unit dihedral angle is greater than an angle threshold, performing edge-folding-based topology optimization to generate a topology optimized mesh; S42: performing local curvature gradient analysis on the topology optimized mesh, dynamically adjusting vertex distribution density according to a comparison result between a curvature gradient value and a density threshold, and generating a density optimized mesh; S43: Performing unit quality evaluation on the density optimized grid, if there are units with quality factors lower than the quality threshold, performing anisotropic local subdivision to generate an optimized anisotropic surface grid.

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