Level set field reconstruction method and system based on three-dimensional finite element mesh and medium

Abstract

The invention discloses a level set field reconstruction method and system based on a three-dimensional finite element grid and a medium. Relates to the technical field of geometric reconstruction. Positioning a space Cartesian grid area intersected with the boundary surface grid based on a separation axis theory; calculating a geometric space point-surface position relation, calculating a directed projection distance from a space Cartesian grid center to a two-dimensional boundary surface grid, and correcting the positive and negative characteristics of a Cartesian grid level set value based on a three-dimensional eight-direction rapid scanning method, so that the grid level set value is consistent with a region boundary value; according to the method, the geometric reconstruction problem of the deformable body which is complex in appearance and free of explicit analytic expression can be efficiently and accurately solved, a coupling approach between a finite element grid and a Cartesian grid is established under a non-conformal grid system, and the flexibility and universality of explicit calculation of a level set function under the Cartesian grid are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geometric reconstruction, in particular to a level set field reconstruction method, system and medium based on a three-dimensional finite element grid. BACKGROUND

[0002] The level set method is a mathematical method for describing, tracking and updating the motion of phase interfaces, which has significant advantages in handling topological changes such as interface splitting, merging or hole generation, and has high efficiency, robustness and scalability in numerical simulation involving the evolution of phase interfaces over time, and has been widely used in scientific fields such as computational fluid dynamics, image processing, topological optimization, etc.

[0003] One of the key difficulties in numerical simulation of gas-liquid-solid multiphase coupling under non-conformal grid system is how to track the solid deformation motion on the Cartesian background grid. In the coupled numerical simulation, the solid deformation body is dynamically solved by finite element technology under the action of fluid external load. Since the solid finite element grid does not directly contact the flow field Cartesian grid, the solid deformation effect after finite element solving cannot be directly fed back to the variable coefficient flow field control equation as a boundary condition. Therefore, mapping the solid deformation to the level set field on the flow field Cartesian grid is an indirect solution to this problem. However, traditional virtual element method, Brinkman volume penalty function method and other non-conformal fluid-solid coupling strategies are only applicable to handling regular shape or rigid solid motion problems with explicit analytical expression, and there is a lack of a general three-dimensional space reconstruction method in the related field to efficiently and accurately establish the mapping relationship between the grid motion of the finite element solved deformation body and the level set function of the deformation body. SUMMARY

[0004] The technical problem to be solved by the present application is that the traditional non-conformal fluid-solid coupling method for tracking solid deformation motion is only applicable to handling regular shape or rigid solid motion problems with explicit analytical expression, and it is difficult to reconstruct the spatial level set field corresponding to the grid motion of the deformation body. The present application aims to provide a level set field reconstruction method, system and medium based on a three-dimensional finite element grid, which improves the method based on the prior art, constructs a finite element grid deformation field of the target three-dimensional entity of the deformation motion, and maps the finite element grid deformation field to the Cartesian background grid to form a corresponding level set field. According to the intersection relationship between the Cartesian grid and the boundary surface grid, the intersection grid set T and the non-intersection grid set F are divided, the level set values of the intersection grid set T are updated based on the mapping relationship, and the level set values of each Cartesian grid in the non-intersection grid set F are corrected. Under the premise of keeping the flow field Cartesian grid and the solid finite element grid independent of each other, the solid interface is continuously and accurately tracked on the Euler grid, avoiding information loss and interpolation error caused by grid mismatch, and significantly improving the reliability of fluid-solid coupling calculation.

[0005] The application is achieved by the following technical solutions: The application provides a level set field reconstruction method based on a three-dimensional finite element grid, comprising: The target three-dimensional entity is divided into a finite element grid, and a boundary surface grid of the three-dimensional entity is extracted from the finite element grid; the boundary surface grid is composed of a plurality of two-dimensional surface grids; A three-dimensional reconstruction region is determined, and a plurality of Cartesian grids are obtained by spatial grid division on the three-dimensional reconstruction region; the three-dimensional reconstruction region contains and is larger than a three-dimensional entity region, The level set values of each Cartesian grid are assigned, the intersection grid set T and the non-intersection grid set F are divided according to the intersection relationship between the Cartesian grid and the boundary surface grid, and the intersection mapping relationship P of each Cartesian grid in the intersection grid set T is obtained; Based on the intersection mapping relationship P, the target surface grid having the intersection relationship with each Cartesian grid in the intersection grid set T is found in the boundary surface grid, and the level set value of the current Cartesian grid is updated based on the projection distance with the minimum modulus between the current Cartesian grid and the corresponding target surface grid in the intersection grid set T. The level set values of each Cartesian grid in the non-intersection grid set F are corrected.

[0006] Further optimization scheme is that the finite element grid is a first-order tetrahedral grid, the surface grid is a two-dimensional first-order triangular grid, the sizes of each Cartesian grid are consistent, and the size of the Cartesian grid is smaller than the size of the finite element grid.

[0007] Further optimization scheme is that the level set value includes a numerical value and a sign value, the numerical value is used to represent the nearest distance from the current spatial position to the surface of the three-dimensional entity, and the sign value is used to represent the inside and outside positions of the current spatial position relative to the three-dimensional entity.

[0008] Further optimization scheme is that the intersection grid set T and the intersection mapping relationship P are obtained by the following method: The level set values of each Cartesian grid are assigned, wherein the sign value is taken as the current spatial position being located outside the three-dimensional entity, and the numerical value is taken as an arbitrary value; Each Cartesian grid is taken as the center to construct a box-shaped control body with a width of 2d; It is judged whether each box-shaped control body intersects with the surface grid in the boundary surface grid, if yes, all the Cartesian grids in the current box-shaped control body are divided into the intersection grid set T, and if not, all the Cartesian grids in the current box-shaped control body are divided into the non-intersection grid set F; The intersection relationship between each Cartesian grid in the intersection grid set T and one or more intersection surface grids is obtained to obtain the intersection mapping relationship P.

[0009] A further optimized solution is that the method for determining whether each box-shaped control volume intersects with the surface mesh in the boundary surface mesh includes: Obtain the normal vectors of all faces of the box-shaped control volume, and all edge vectors of the mesh of each face; Using the normal vector and edge vector of the surface as the separation axis, the projection intervals of the box-shaped control body and the surface mesh along each separation axis are detected. If the projection intervals of the current box-shaped control body and the current surface mesh along all separation axes overlap, it is determined that the current box-shaped control body and the current surface mesh intersect.

[0010] A further optimized scheme involves finding the target surface mesh that intersects with each Cartesian mesh in the intersecting mesh set T based on the intersection mapping relationship P. Then, based on the projection distance with the smallest modulus between the current Cartesian mesh and the corresponding target surface mesh in the intersecting mesh set T, the level set value of the current Cartesian mesh is updated. This includes the following method: Calculate the unit normal vector of each face mesh in the boundary surface mesh; Based on the intersection mapping relationship P, find the target surface mesh in the boundary surface mesh that has an intersection relationship with each Cartesian mesh in the intersecting mesh set T; Calculate the location of the center point of the Cartesian grid by combining the unit normal vectors of each face. C Directed projection distance results to each target surface grid: Process L: Position the points of Cartesian grid i C Projecting onto the plane of the target surface grid j, if the projection point is located inside the target surface grid j, then the projection distance is taken as the location point. C The perpendicular distance to the target surface grid j is calculated, and combined with the unit normal vector of the target surface grid j, the directed projection distance is obtained. If the projection point falls outside or on the boundary of the target surface grid j, the nearest point K with the smallest distance to the position point C is first searched on the edges and vertices of all surface grids. Then, the angle-weighted pseudo-vector is calculated based on the nearest point K. n k Based on angle-weighted pseudo-vectors n k The projected distance is obtained by projection. If Cartesian grid i has multiple target surface grids, repeat process L to obtain multiple directed projection distances, and take the directed projection distance with the smallest modulus as the directed projection distance of Cartesian grid i. Update the Cartesian grid level set values ​​based on the directed projection distance results, according to the angle-weighted pseudo-vector. n k The sign value of the Cartesian grid level set is updated in the direction of the update.

[0011] A further optimized solution is to use the nearest point K Calculate the angle-weighted pseudo-vector based on the reference.n k Based on angle-weighted pseudo-vectors n k The projected distance is obtained by projection; including methods: Find the nearest point K Let Δ be the mesh of all faces of a vertex. i ( i =1,2,…, n );in, n Indicates the nearest point K The total number of face grids at each vertex; From the nearest point K Determine the outgoing mesh Δ i First edge vector v i1 = V i1 – K Second side vector v i2 = V i2 – K ,in V i1 and V i2 They are respectively surface mesh Δ i The other two vertices; The angle between the first and second side vectors is calculated using the following formula. :

[0012] Here, arccos() represents the inverse cosine function; ||*|| represents the modulus operation of a vector. With the included angle As a surface mesh Δ i The angle at the nearest point K Calculate the surface mesh Δ i unit normal vector n i ; The angles of all face meshes with the nearest vertex K are weighted, superimposed, and normalized to obtain an angle-weighted pseudo-vector. n k : ; Angle-weighted pseudo-vector n k Replace surface mesh Δ i The directed projected distance is obtained by projecting the normal vector onto the target vector. ;in, d denotes center point C To the surface mesh Δ iThe projection distance.

[0013] Further optimization scheme is that the level set value of each Cartesian grid in the disjunctive grid set F is modified. Sweep all Cartesian grids in the disjunctive grid set F along different arrangement directions of the Cartesian grids: compare the sign value of the Cartesian grid i with the sign value of the adjacent Cartesian grid j, and when the sign value of the Cartesian grid i is inconsistent with the sign value of the Cartesian grid j, modify the sign value of the Cartesian grid i to the sign value of the Cartesian grid j.

[0014] The scheme also provides a level set field reconstruction system method based on three-dimensional finite element grids, which is used for implementing the level set field reconstruction method based on three-dimensional finite element grids. The first grid division module is used for dividing the target three-dimensional entity into finite element grids and extracting the boundary surface grid of the three-dimensional entity from the finite element grids; the boundary surface grid is composed of a plurality of two-dimensional surface grids. The second grid division module is used for determining a three-dimensional reconstruction region and performing spatial grid division on the three-dimensional reconstruction region to obtain a plurality of Cartesian grids; the three-dimensional reconstruction region contains and is larger than the three-dimensional entity region. The mapping module is used for assigning a level set value to each Cartesian grid, dividing the intersection grid set T and the disjunctive grid set F according to the intersection relationship between the Cartesian grid and the boundary surface grid, and obtaining the intersection mapping relationship P of each Cartesian grid in the intersection grid set T. The calculation module is used for finding the target surface grid having the intersection relationship with each Cartesian grid in the intersection grid set T in the boundary surface grid based on the intersection mapping relationship P, and updating the level set value of the current Cartesian grid based on the projection distance with the minimum modulus between the current Cartesian grid in the intersection grid set T and the corresponding target surface grid. The modification module is used for modifying the level set value of each Cartesian grid in the disjunctive grid set F.

[0015] The scheme also provides a computer readable medium having a computer program stored thereon, and the computer program is executed by a processor to implement the level set field reconstruction method based on three-dimensional finite element grids.

[0016] Compared with the prior art, the present application has the following advantages and beneficial effects: 1. The three-dimensional finite element grid-based level set field reconstruction method, system and medium provided by the application; the method is improved on the basis of the prior art, a finite element grid deformation field of a target three-dimensional entity in deformation is constructed, the finite element grid deformation field is mapped into a Cartesian background grid to form a corresponding level set field, an intersection grid set T and a non-intersection grid set F are divided according to the intersection relationship between the Cartesian grid and the boundary surface grid, the level set values of the intersection grid set T are updated based on the mapping relationship, and the level set values of each Cartesian grid in the non-intersection grid set F are corrected; under the premise that the Cartesian grid of the flow field and the solid finite element grid are independent of each other, the solid interface is continuously and accurately tracked on the Euler grid, information loss and interpolation errors caused by grid mismatch are avoided, and the reliability of the fluid-solid coupling calculation is significantly improved.

[0017] 2. The three-dimensional finite element grid-based level set field reconstruction method, system and medium provided by the application; based on the obtained level set field and the regularized Heaviside function, the distribution law of physical properties such as flow field density and viscosity can be further determined, which is helpful for solving the variable coefficient control equation on the Euler grid to obtain flow field related information.

[0018] 3. The three-dimensional finite element grid-based level set field reconstruction method, system and medium provided by the application; based on the obtained level set field and the regularized Heaviside function, the distribution law of physical properties such as flow field density and viscosity can be further determined, which is helpful for solving the variable coefficient control equation on the Euler grid to obtain flow field related information.

[0019] 4. The three-dimensional finite element grid-based level set field reconstruction method, system and medium provided by the application; the core technical concept is to keep the Cartesian background grid fixed and rely on the level set function to capture the deformed interface of the target three-dimensional entity in real time; compared with the traditional grid which needs to be dynamically reconstructed or stretched with the deformation of the entity, the present scheme does not need to deform or regrid the background grid, and can avoid frequent redivision operations and the grid mismatch and interpolation errors caused thereby; compared with the existing virtual element method, Brinkman volume penalty method and other non-conformal grid coupling strategies, the present method does not need to introduce virtual elements or penalty parameters, and also does not need to adjust the form of the flow field control equation, thereby avoiding problems such as ambiguous virtual element boundary and difficult adjustment of the penalty coefficient. The method not only supports arbitrary large deformation and topological change, but also can realize high-precision capture at complex curved surfaces, sharp corners and small features, and significantly improves the accuracy of interface positioning and the continuity of numerical fields. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor. In the drawings: Figure 1 A flowchart of a level set field reconstruction method based on a three-dimensional finite element mesh; Figure 2 A schematic diagram of numerical changes of a level set field in a local plane of a three-dimensional reconstruction region; Figure 3 A schematic diagram of a level set field reconstruction system structure based on a three-dimensional finite element mesh. DETAILED DESCRIPTION

[0021] In order to make the objects, technical solutions and advantages of the present application clearer, the following will further describe the present application in combination with embodiments and drawings. The exemplary embodiments of the present application and their descriptions are only used to explain the present application, and should not be regarded as a limitation on the present application.

[0022] The traditional non-conformal fluid-structure coupling method for tracking solid deformation motion is only applicable to processing rigid solid motion with regular shape or explicit analytical expression, and is difficult to reconstruct a spatial level set field corresponding to the mesh motion of a deformed body. In view of this, the present application provides the following embodiments to solve the above technical problems: Embodiment 1 The present embodiment provides a level set field reconstruction method based on a three-dimensional finite element mesh, as shown in Figure 1 The method comprises the following steps.

[0023] Step 1: dividing a target three-dimensional entity into a finite element mesh, and extracting a boundary surface mesh of the three-dimensional entity from the finite element mesh; the boundary surface mesh is composed of a plurality of two-dimensional surface meshes; in the present application, the finite element mesh is a first-order tetrahedral mesh, and the finite element mesh is generated based on an existing mesh processing software, such as an open source software Gmsh; the method of the present application does not support high-order or hexahedral meshes, and therefore, non-first-order tetrahedral meshes need to be re-divided into first-order tetrahedral meshes in the mesh processing software. In the mesh processing software, the boundary surface mesh in the first-order tetrahedral mesh is extracted by naming and grouping, and the boundary surface mesh of the three-dimensional entity is extracted, which is composed of a plurality of surface meshes. The surface mesh in the present embodiment is a two-dimensional first-order triangular mesh.

[0024] Step 2: determining a three-dimensional reconstruction region, and performing spatial mesh division on the three-dimensional reconstruction region to obtain a plurality of Cartesian meshes; the three-dimensional reconstruction region contains and is larger than a three-dimensional entity region; The geometric dimensions of the 3D reconstruction region should be larger than the target 3D entity, and the spatial position of the target 3D entity should be completely contained within the 3D reconstruction region. In this embodiment, the spatial Cartesian mesh is a 3D structured mesh, and the length, width, and height of the mesh are denoted as {dx, dy, dz}, with the specific value relationship being dx=dy=dz. The size of each Cartesian mesh within the 3D reconstruction region is consistent, and the size of the Cartesian mesh should be smaller than the size of the finite element mesh, so that each finite element mesh contains at least one Cartesian mesh in the background mesh, ensuring accurate capture of the fine boundary features of the deformed entity and reducing the calculation error of the angle-weighted pseudo-vector. Specifically, in this embodiment, the finite element mesh size is 2.0×dx.

[0025] Step three involves assigning level set values ​​to each Cartesian mesh. Based on the intersection relationship between the Cartesian mesh and the boundary surface mesh, an intersecting mesh set T and a non-intersecting mesh set F are created. The intersection mapping relationship P of each Cartesian mesh in the intersecting mesh set T is then obtained. The level set values ​​in step three include numerical and sign values. The numerical value represents the closest distance from the current spatial position to the surface of the 3D entity, while the sign value represents the current spatial position relative to the interior or exterior of the 3D entity. In this embodiment, a positive sign value indicates that the current spatial position is outside the surface of the 3D entity, and a negative sign value indicates that the current spatial position is inside the surface of the 3D entity.

[0026] The methods for obtaining the intersecting mesh set T and the intersecting mapping relationship P in step three include: S31, assign level set values ​​to each Cartesian mesh, where the sign value is taken as the current spatial position being outside the 3D entity; the numerical value is arbitrary; the level set value can be any large positive value. In this embodiment, the initial value of the level set value is taken as... a = +1, after initialization, the horizontal field value in the local plane of the 3D reconstruction region is as follows: Figure 2 As shown in (a); S32, construct a box-shaped control volume with a width of 2d centered on each Cartesian grid; the three-dimensional geometric dimensions of the box-shaped control volume are {2... d ×dx, 2 d ×dy, 2 d ×dz}, in this embodiment d With a value of 1.5, the local plane of the box-shaped control volume within the 3D reconstruction region is as follows: Figure 2 As shown in (b); S33, determine whether each box-shaped control volume intersects with the surface mesh in the boundary surface mesh. If so, divide all Cartesian meshes in the current box-shaped control volume into the intersecting mesh set T; otherwise, divide all Cartesian meshes in the current box-shaped control volume into the non-intersecting mesh set F. In this embodiment, the intersecting mesh set T divided in the local plane of the 3D reconstruction region is as follows: Figure 2 As shown in (c); In step S33, the method of judging whether each box-shaped control body intersects with a face mesh in the boundary face mesh comprises: S331, obtaining normal vectors of all faces of the box-shaped control body and all edge vectors of the face mesh; S332, taking the normal vectors of the faces and the edge vectors as separation axes, detecting projection intervals of the box-shaped control body and the face mesh along each separation axis, and judging that the current box-shaped control body intersects with the current face mesh if there is an overlap between the projection intervals of the current box-shaped control body and the current face mesh along all separation axes.

[0027] S34, obtaining intersection relationships between each Cartesian mesh in the intersection mesh set T and one or more intersecting face meshes to obtain an intersection mapping relationship P.

[0028] Step four, finding target face meshes having intersection relationships with each Cartesian mesh in the intersection mesh set T in the boundary face mesh based on the intersection mapping relationship P, and updating a level set value of a current Cartesian mesh based on a minimum projection distance between the current Cartesian mesh and the corresponding target face mesh in the intersection mesh set T; the step specifically comprises the following method: S41, calculating unit normal vectors of each face mesh in the boundary face mesh; the step specifically comprises the following method: traversing each face mesh, calculating any two edge vectors according to spatial positions of three vertices of the face mesh, and calculating a unit normal vector of the face mesh through vector cross multiplication; in this embodiment, a unit normal vector of a face mesh in a local plane of the three-dimensional reconstruction region is as shown in (d); Figure 2 S42, traversing Cartesian meshes in the intersection mesh set T, and finding target face meshes having intersection relationships with each Cartesian mesh in the intersection mesh set T in the boundary face mesh based on the intersection mapping relationship P; S43, combining the unit normal vectors of each face mesh, and calculating a position point C of a center of the Cartesian mesh to a directed projection distance result of the position point C to each target face mesh j: C Process L: projecting the position point C of the Cartesian mesh i to a plane of the target face mesh j, if the projection point is located inside the target face mesh j, then the projection distance is taken as a vertical distance from the position point C to the plane of the target face mesh j, and a directed projection distance is obtained in combination with the unit normal vector of the target face mesh j; if the projection point falls outside or on the boundary of the target face mesh j, then the nearest point N to the position point C is searched on all edge lines and vertices of the face mesh, and then an angle-weighted pseudo vector is calculated based on the nearest point N and the position point C: C C K K n k n ​​​​​​​k The projected distance is obtained by projection. The nearest point K Calculate the angle-weighted pseudo-vector based on the reference. n k Based on angle-weighted pseudo-vectors n k The projected distance is obtained by projection; including methods: S431, find the nearest point K Let Δ be the mesh of all faces of a vertex. i ( i =1,2,…, n );in, n Indicates the nearest point K The total number of face grids at each vertex; S432, from the nearest point K Determine the outgoing mesh Δ i First edge vector v i1 = V i1 – K Second side vector v i2 = V i2 – K ,in V i1 and V i2 They are respectively surface mesh Δ i The other two vertices; S433, calculate the angle between the first side vector and the second side vector according to the following formula. :

[0029] Here, arccos() represents the inverse cosine function; ||*|| represents the modulus operation of a vector. S434, with an included angle As a surface mesh Δ i The angle at the nearest point K Calculate the surface mesh Δ i unit normal vector n i The sign of the unit normal is determined according to the right-hand rule. S435: Weighted summation and normalization of the angles between all face meshes with the nearest vertex K, resulting in an angle-weighted pseudo-vector. n k : ; S436, using angle-weighted pseudovectors nk Replace surface mesh Δ i The directed projected distance is obtained by projecting the normal vector onto the target vector. ;in, d denotes center point C To the surface mesh Δ i The projection distance. In this embodiment, the projection distance of the Cartesian grid center point is calculated as follows: Figure 2 As shown in (e); If Cartesian mesh i has only one target surface mesh, the directed projection distance of Cartesian mesh i can be directly obtained according to process L; if Cartesian mesh i has multiple target surface meshes, process L is repeated to obtain multiple directed projection distances, and the directed projection distance with the smallest modulus is taken as the directed projection distance of Cartesian mesh i. S44, update the Cartesian grid level set values ​​based on the directed projection distance results, and based on the angle-weighted pseudo-vector. n k The direction updates the sign value of the Cartesian grid level set. Specifically, the magnitude of the directed projection distance is equal to the projected distance, and the sign (direction) of the directed projection distance is determined by the angle-weighted pseudo-vector. n k Determine if the center point of the Cartesian grid is [value missing]. C On the outside of the face grid ( n k (where the vector is positive), the directed projection distance is equal to + d If the center point of the Cartesian grid C Inside the surface mesh, the directed projection distance is equal to - d .

[0030] Step 5: Traverse each Cartesian grid in the set of disjoint grids F, and correct the level set values ​​of each Cartesian grid in the set of disjoint grids F; this step specifically includes the following methods: Sweep through all Cartesian grids in the set of disjoint grids F one by one along different arrangement directions of the Cartesian grid: compare the sign values ​​of Cartesian grid i with those of its neighboring Cartesian grid j. When the sign values ​​of Cartesian grid i and Cartesian grid j are inconsistent, correct the sign value of Cartesian grid i to the sign value of Cartesian grid j.

[0031] The correction strategy follows these principles: Except for boundary mesh regions, the Cartesian mesh sign should not exhibit inconsistent sign jumps; in this embodiment, the outermost mesh of the transition region is set as the boundary, such as... Figure 2(f) the positive and negative of the signed distance field of the Cartesian grid outside the boundary should be consistent with the positive and negative of the boundary grid. The level set value (including size and direction) of the Cartesian grid in the intersected grid set T has been determined in the above process; the level set value of the Cartesian grid in the non-intersected grid set F needs to be corrected, and the all Cartesian grids in the non-intersected grid set F are scanned point by point, and for each Cartesian grid in the non-intersected grid set F, the grid is compared with the adjacent grid in a certain direction. Each Cartesian grid has six main directions of +X, -X, +Y, -Y, +Z and -Z, and the adjacent Cartesian grid j in the embodiment refers to the adjacent Cartesian grid sharing the boundary surface with the adjacent Cartesian grid i in the selected direction, and theoretically, there are six adjacent Cartesian grids for a three-dimensional Cartesian grid. After completing the scanning in one direction, the same operation is repeated for the remaining five directions; after the scanning in all directions is completed, it can be ensured that the sign information of each Cartesian grid in the non-intersected grid set F is transmitted and covered by the nearest boundary unit or the corrected neighborhood unit, so that the sign isolation and jump in the solid interior are eliminated, and the continuous consistency of the entire Cartesian grid signed distance field is realized.

[0032] The finally obtained reconstructed level set field presents a strip distribution rule, the grid level set field in the intersected grid set T has a signed distance attribute, the grid level set field not in the intersected grid set T but located outside the three-dimensional entity of the reconstruction region takes the initial value a The grid level set field not in the intersected grid set T but located inside the three-dimensional entity of the reconstruction region takes the initial value -a The level set field value in the local plane of the reconstruction region in the embodiment is as shown in Figure 2 (f) shown.

[0033] The solid level set field reconstruction technology provided by the scheme can be used in fluid-structure coupling analysis of a complex deformed structure; under the framework of a complete Euler type algorithm such as the immersed boundary method, the scheme maps the finite element grid deformation field to the Cartesian background grid and forms the corresponding level set field, based on the obtained level set field and the regularized Heaviside function, the distribution rule of the density, viscosity and other physical properties of the flow field can be further determined, which is helpful for solving the variable coefficient control equation on the Euler grid to obtain the information related to the flow field.

[0034] The method provided by the scheme is an important link in the non-conformal fluid-structure coupling algorithm framework, which realizes the continuous and accurate tracking of the solid interface on the Euler grid under the premise that the flow field Cartesian grid and the solid finite element grid are independent of each other, avoids the information loss and interpolation error caused by the grid mismatch, and significantly improves the reliability of the fluid-structure coupling calculation.

[0035] Embodiment 2 The embodiment provides a level set field reconstruction system method based on a three-dimensional finite element grid, as shown in Figure 3 The level set field reconstruction method based on the three-dimensional finite element grid is realized. A first grid division module is used for dividing a target three-dimensional entity into a finite element grid and extracting a boundary surface grid of the three-dimensional entity from the finite element grid; the boundary surface grid is composed of a plurality of two-dimensional surface grids. A second grid division module is used for determining a three-dimensional reconstruction region and performing spatial grid division on the three-dimensional reconstruction region to obtain a plurality of Cartesian grids; the three-dimensional reconstruction region contains and is larger than a three-dimensional entity region, A mapping module is used for assigning a level set value to each Cartesian grid, dividing an intersection grid set T and a non-intersection grid set F according to intersection relationships of the Cartesian grids and the boundary surface grid, and obtaining an intersection mapping relationship P of each Cartesian grid in the intersection grid set T; A calculation module is used for finding a target surface grid having an intersection relationship with each Cartesian grid in the intersection grid set T in the boundary surface grid based on the intersection mapping relationship P, and updating a level set value of a current Cartesian grid based on a projection distance with minimum module length between the current Cartesian grid and the corresponding target surface grid in the intersection grid set T. A correction module is used for correcting the level set values of the Cartesian grids in the non-intersection grid set F.

[0036] Embodiment 3 The embodiment provides a computer readable medium, which stores a computer program and the computer program is executed by a processor to realize the level set field reconstruction method based on the three-dimensional finite element grid. Step one, a target three-dimensional entity is divided into a finite element grid, and a boundary surface grid of the three-dimensional entity is extracted from the finite element grid; the boundary surface grid is composed of a plurality of two-dimensional surface grids. Step two, a three-dimensional reconstruction region is determined, and spatial grid division is performed on the three-dimensional reconstruction region to obtain a plurality of Cartesian grids; the three-dimensional reconstruction region contains and is larger than a three-dimensional entity region, Step three, a level set value is assigned to each Cartesian grid, an intersection grid set T and a non-intersection grid set F are divided according to intersection relationships of the Cartesian grids and the boundary surface grid, and an intersection mapping relationship P of each Cartesian grid in the intersection grid set T is obtained. Step four, a target surface grid having an intersection relationship with each Cartesian grid in the intersection grid set T is found in the boundary surface grid based on the intersection mapping relationship P, and a level set value of a current Cartesian grid is updated based on a projection distance with minimum module length between the current Cartesian grid and the corresponding target surface grid in the intersection grid set T. Step five, correct the level set value of each Cartesian grid in the disjoint grid set F.

[0037] The scheme extracts the two-dimensional finite element boundary surface grid of the target three-dimensional entity, positions the spatial Cartesian grid region intersecting with the boundary surface grid based on the separate axis theory, calculates the directed projection distance from the center of the spatial Cartesian grid to the two-dimensional boundary surface grid based on the spatial point-surface position relationship of computational geometry, and corrects the positive and negative of the level set value of the Cartesian grid based on the three-dimensional eight-direction fast scanning method, so that the grid level set value is consistent with the region boundary value. The scheme can efficiently and accurately process the geometric reconstruction problem of a deformed body with complex shape and without explicit analytical expression, establishes a coupling approach between the finite element grid and the Cartesian grid under a non-conformal grid system, and improves the flexibility and universality of the explicit calculation of the level set function under the Cartesian grid.

[0038] The above specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A horizontal field reconstruction method based on three-dimensional finite element mesh, characterized in that, include: 。 The target 3D entity is divided into finite element meshes, and the boundary surface mesh of the 3D entity is extracted from the finite element meshes. The boundary surface mesh is composed of multiple two-dimensional surface meshes; A 3D reconstruction region is determined, and the region is then divided into multiple Cartesian meshes; the 3D reconstruction region includes and is larger than the 3D solid region. Assign horizontal set values ​​to each Cartesian mesh, divide the mesh into an intersecting mesh set T and a non-intersecting mesh set F according to the intersection relationship between the Cartesian mesh and the boundary surface mesh, and obtain the intersection mapping relationship P of each Cartesian mesh in the intersecting mesh set T; Based on the intersection mapping relationship P, find the target surface mesh that has an intersection relationship with each Cartesian mesh in the intersection mesh set T in the boundary surface mesh. Based on the projection distance with the smallest modulus between the current Cartesian mesh and the corresponding target surface mesh in the intersection mesh set T, update the level set value of the current Cartesian mesh. Correct the level set values ​​of each Cartesian grid in the set of disjoint grids F.

2. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 1, characterized in that, The finite element mesh is a first-order tetrahedral mesh, and the surface mesh is a two-dimensional first-order triangular mesh; the dimensions of each Cartesian mesh are consistent, and the dimensions of the Cartesian mesh are smaller than the dimensions of the finite element mesh.

3. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 2, characterized in that, The level set values ​​include numerical and symbolic values. The numerical values ​​are used to represent the nearest distance from the current spatial location to the surface of the three-dimensional entity, and the symbolic values ​​are used to represent the inward and outward positions of the current spatial location relative to the three-dimensional entity.

4. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 3, characterized in that, The methods for obtaining the intersecting mesh set T and the intersecting mapping relationship P include: Assign horizontal set values ​​to each Cartesian mesh, where the sign value is taken as the current spatial position being outside the 3D entity; the numerical value can be any value. Construct a box-shaped control volume with a width of 2d centered on each Cartesian grid; Determine whether each box-shaped control volume intersects with the face mesh in the boundary surface mesh. If so, assign all Cartesian meshes in the current box-shaped control volume to the intersecting mesh set T; otherwise, assign all Cartesian meshes in the current box-shaped control volume to the non-intersecting mesh set F. The intersection mapping relationship P is obtained by obtaining the intersection relationship between each Cartesian grid in the set of intersecting grids T and one or more intersecting surface grids.

5. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 4, characterized in that, The determination is made as to whether each box-shaped control body intersects with the surface mesh in the boundary surface mesh; Including methods: Obtain the normal vectors of all faces of the box-shaped control volume, and all edge vectors of the mesh of each face; Using the normal vector and edge vector of the surface as the separation axis, the projection intervals of the box-shaped control body and the surface mesh along each separation axis are detected. If the projection intervals of the current box-shaped control body and the current surface mesh along all separation axes overlap, it is determined that the current box-shaped control body and the current surface mesh intersect.

6. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 3, characterized in that, Based on the intersection mapping relationship P, the target surface mesh that intersects with each Cartesian mesh in the intersection mesh set T is found in the boundary surface mesh. The level set value of the current Cartesian mesh is updated based on the projection distance with the smallest modulus between the current Cartesian mesh and the corresponding target surface mesh in the intersection mesh set T. This includes... method: Calculate the unit normal vector of each face mesh in the boundary surface mesh; Based on the intersection mapping relationship P, find the target surface mesh in the boundary surface mesh that has an intersection relationship with each Cartesian mesh in the intersecting mesh set T; Calculate the location of the center point of the Cartesian grid by combining the unit normal vectors of each face. C Directed projection distance results to each target surface grid: Process L: Position the points of Cartesian grid i C Projecting onto the plane of the target surface grid j, if the projection point is located inside the target surface grid j, then the projection distance is taken as the location point. C The perpendicular distance to the target surface grid j is calculated, and combined with the unit normal vector of the target surface grid j, the directed projection distance is obtained. If the projection point falls outside or on the boundary of the target surface grid j, the nearest point K with the smallest distance to the position point C is first searched on the edges and vertices of all surface grids. Then, the angle-weighted pseudo-vector is calculated based on the nearest point K. n k Based on angle-weighted pseudo-vectors n k The projected distance is obtained by projection. If Cartesian grid i has multiple target surface grids, repeat process L to obtain multiple directed projection distances, and take the directed projection distance with the smallest modulus as the directed projection distance of Cartesian grid i. Update the Cartesian grid level set values ​​based on the directed projection distance results, according to the angle-weighted pseudo-vector. n k The sign value of the Cartesian grid level set is updated in the direction of the update.

7. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 6, characterized in that, The angle-weighted pseudo-vector is calculated based on the nearest point K. n k Based on angle-weighted pseudo-vectors n k Projection is performed to obtain the directed projected distance; including method: Find the nearest point K Let Δ be the mesh of all faces of a vertex. i ( i =1,2,…, n );in, n Indicates the nearest point K The total number of face grids at each vertex; From the nearest point K Determine the outgoing mesh Δ i First edge vector v i1 = V i1 – K Second side vector v i2 = V i2 – K ,in V i1 and V i2 They are respectively surface mesh Δ i The other two vertices; The angle between the first and second side vectors is calculated using the following formula. : Here, arccos() represents the inverse cosine function; ||*|| represents the modulus operation of a vector. With the included angle As a surface mesh Δ i The angle at the nearest point K Calculate the surface mesh Δ i unit normal vector n i ; The angles of all face meshes with the nearest vertex K are weighted, superimposed, and normalized to obtain an angle-weighted pseudo-vector. n k : ; Angle-weighted pseudo-vector n k Replace surface mesh Δ i The directed projected distance is obtained by projecting the normal vector onto the target vector. ;in, d represents center point C To the surface mesh Δ i The projected distance.

8. The horizontal field reconstruction method based on a three-dimensional finite element mesh according to claim 3, characterized in that, The level set values ​​of each Cartesian grid in the set of disjoint grids F are corrected; Including methods: Sweep through all Cartesian grids in the set of disjoint grids F one by one along different arrangement directions of the Cartesian grid: compare the sign values ​​of Cartesian grid i with those of its neighboring Cartesian grid j. When the sign values ​​of Cartesian grid i and Cartesian grid j are inconsistent, correct the sign value of Cartesian grid i to the sign value of Cartesian grid j.

9. A horizontal field reconstruction system method based on three-dimensional finite element mesh, characterized in that, The method for reconstructing a horizontal field based on a three-dimensional finite element mesh as described in any one of claims 1-8 includes: The first mesh generation module is used to divide the target three-dimensional entity into finite element meshes and extract the boundary surface mesh of the three-dimensional entity from the finite element meshes; the boundary surface mesh is composed of multiple two-dimensional surface meshes. The second mesh generation module is used to determine the 3D reconstruction region and perform spatial mesh generation on the 3D reconstruction region to obtain multiple Cartesian meshes; the 3D reconstruction region includes and is larger than the 3D solid region. The mapping module is used to assign horizontal set values ​​to each Cartesian mesh, divide the intersecting mesh set T and the non-intersecting mesh set F according to the intersection relationship between the Cartesian mesh and the boundary surface mesh, and obtain the intersection mapping relationship P of each Cartesian mesh in the intersecting mesh set T; The calculation module is used to find the target surface mesh that intersects with each Cartesian mesh in the intersecting mesh set T in the boundary surface mesh based on the intersection mapping relationship P, and update the level set value of the current Cartesian mesh based on the minimum projection distance between the current Cartesian mesh and the corresponding target surface mesh in the intersecting mesh set T. The correction module is used to correct the level set values ​​of each Cartesian grid in the set of disjoint grids F.

10. A computer-readable medium having a computer program stored thereon, characterized in that, The computer program, when executed by a processor, can implement the horizontal field reconstruction method based on a three-dimensional finite element mesh as described in any one of claims 1-8.

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