Research On Mesh Generation Of Boundary Face Method And Its Application In Spherical Subdivision

The boundary face method(BFM)based on the boundary integral equation(BIE)exhibits some extraordinary merits.Generally,the BFM only require to discrete the surfaces of problem domain and can employ discontinuous element.Hence,the surface mesh generation based on BFM is independent of each other,so that the mesh generation method can be much more flexible.In order to make full use of this advantage of BFM,a program toolkit of surface mesh generation using C++ language is developed.The toolkit integrates various surface mesh generation methods,various size control methods,boundary curve adaptive discretization,feature recognition based on mesh generation method and mesh data management.In addition,the mesh generation methods are used to element subdivision which resolves the problem of nearly singular integrals in BFM.As a result,the following studies are carried out in this dissertation:(1)In order to make full use of the advantages of structured mesh generated by mapping,a new method based on block division is proposed.First,the structured background mesh is generated by mapping and the location of small feature such as hole and keyway is determined.Then the meshes which are covered by small feature are eliminated from background mesh and a cavity is generated around the small feature.As the cavity is relatively small and irregular,the unstructured mesh can be generated in this region.At this point,the mesh of target domain is divided into two parts.One is the unstructured mesh in the cavity and the other is valid background mesh.The method needs to combine with other advancing front methods,which are used to generated unstructured mesh in the cavity.It is capable of preserving the advantages of structured mesh's high efficiency,high quality and uniform distribution of the mesh and controllable mesh density and unstructured mesh's powerful geometric adaptive capacity.(2)Since the quadrilateral mesh generation method is less mature relative to the triangular mesh,in order to generate the good quality quadrilateral mesh,a new advancing front method with constraint is proposed.The method that is based on the idea of advancing front is a kind of indirect method,which the triangular mesh is generated firstly,and then the quadrilateral mesh is generated by merging the triangular mesh.The hard part of the indirect method is that the isolated triangles may be generated on the merging procedure.To solve this,some constraining conditions are imposed on the advancing procedure,which could be sufficient to avoid generating isolated triangles,so that the all good quality quadrilateral mesh can be achieved.(3)To generate adaptive surface mesh for complex solid surface automatically,various size control methods are implemented in the dissertation.First,the size control method based on octree is implemented.This method can recognize curvature feature and small feature,moreover,the efficiency of this control method is high.But the disadvantage of this control method is that it can not recognize proximity feature.Then in order to recognize proximity feature,the size control method based on proximity feature is implemented.However,this control method can not recognize small feature,and to calculate the size of a given point,the triangle that contains the given point is searched in the Delauany triangulation network,while the searching procedure is time consuming.To improve the search efficiency,a search mechanism based on K-d Tree is proposed.As the above two methods have some flaws,by combining the advantages of both methods,a new control method based on proximity feature octree is proposed.The new control mode could recognize curvature feature,small feature and proximity feature,and the efficiency of this control method is high.Besides,the new control method can be used for solid mesh generation.(4)The structured mesh has the advantages of good quality,high efficiency,simple data structure,controllable mesh density and high computational efficiency,while the main drawback of structured mesh is the narrow scope of application which can only be used to regular geometric shapes.For the complex domain,the domain is needed to be decomposed into some subdomains,and then the mesh is generated in each subdomain.However,the decomposition process is time consuming which is not suitable for large-scale computation.To solve this,a block structured mesh generation method based on subdomain decomposition is proposed.Some exploratory rules are used to decompose the complex domain,and then structured mesh is generated in each subdomain.Though the method can achieve a certain degree of automation,it is not a general mesh generation method.Then a general block structured mesh generation method based on axis decomposition is implemented.The medial axis that is extracted based on constrained Delaunay triangulation network is used to decompose the complex domain,and then the structured mesh is generated in each subdomain.This method is a general method which can be applied to any domain.(5)The program for automatically generating adaptive surface mesh is developed.In general,adaptive mesh generation is primarily concerned with adaptive size control.Various size control methods are implemented in the dissertation which can achieve the size of any point on the target domain.Additionally,the surface mesh used to BFM is independent of each other.Based on this,a feature recognition technology based on mesh generation method is proposed.Through feature recognition,an appropriate mesh generation method is selected to generate mesh,so that the adaptive method of mesh generation is realized.The mesh generation method toolkit can generate high quality,uniform transitional surface mesh for any complex target domain.(6)In order to calculate the nearly singular integrals in the BFM,a general adaptive subdivision scheme based on the idea of advancing front is proposed.A sequence of spheres with decreasing radius is used to intersect with the element,and then the good quality patches are generated by advancing front method between the adjacent two spheres.The method is applicable to any shape of element with arbitrary location of the source point.With equivalent number of Gaussian points,the calculation accuracy obtained using this method is significantly improved.Moreover,the numerical stability obtained by this method is better than other traditional methods.