Block-controllable Structural Mesh Generation Method Based On Frame Field

Mesh generation is a pre-processing step in numerical simulation techniques,i.e.,the finite element method,the finite volume method,and the finite difference method.For complex geometries,mesh generation is still the main performance bottleneck in the whole numerical simulation process.In 2D,quadrilateral mesh normally has higher solution accuracy and lower solution freedom than triangular mesh,thus it is preferred in the numerical simulation.Nevertheless,it remains a challenging task to create a high-quality quadrilateral mesh automatically,especially for complex geometries.An alternate way for quadrilateral mesh generation is to first partition the domain into sub-regions which are often much simpler than the original domain,and then generate quadrilateral meshes for each sub-region individually.However,for complex geometries,the domain decomposition is as difficult as the quadrilateral mesh generation itself.Automatic,controllable,and high-quality domain decomposition remains an open issue.Currently,the generation of quadrilateral mesh for complex geometries mainly relies on the manual decomposition of the complex domain into regular sub-regions.The introduction of the manual work not only requires engineers to have strong engineering experience but also tends to be time consuming and error-prone.In this paper,a new quadrilateral mesh generation based on domain partition is proposed by analyzing the cross-field over the problem domain governed by two Laplacian equations.Based on the cross-filed theory,singular points of the cross-filed are identified and streamlines emanating from these points are computed as lines to partition the problem domain into a set of meshable subdomains.Compared with other methods,our method provides better control over mesh topology,leading to better mesh quality.The main contributions of this paper are:(1)An automatic decomposition approach is proposed for 2D domains based on solving a vector field.It enables the automatic generation of high-quality block-structured quadrilateral meshes in arbitrary 2D domains.Firstly,a vector field that covers the entire problem domain is obtained by solving the Laplace-type governing equations with the boundary element method(BEM).The vector field also reflects the requirements of users on the generation of boundary aligned quadrilateral elements.Next,the vector field is converted into a frame field by using the basic map between these two fields.Finally,the problem domain is decomposed into several four-sided sub-regions by analyzing the singularities of the frame field,and a block-structured quadrilateral mesh is created by meshing the sub-regions individually with the mapping method.The effectiveness and reliability of the proposed method are verified with complex examples.(2)To meet the requirements of constrained mesh generation,a multiple constrained domain automatic decomposition framework based on frame field is proposed.The automatic decomposition framework of multiple constraint domain is realized by expanding the two-dimensional domain automatic decomposition method.In practical applications,most of the objects are multiple materials,and this feature needs careful consideration in modeling and performance analysis.By keeping the boundary of the model unchanged,the method identifies the common spaces of each material block,such as point constraints,line constraints,curvature constraints,and applies different types of constraints according to user requirements.Then,mathematical models are established and solved,achieving multiple constraint domain decompositions.The reliability and practicability of the proposed method are verified by the mesh generation example of the multiple constraint model domain.