Automatic Hybrid Mesh Generation For Viscous Flow Simulations With Complex Geometries

Among the different mesh types,prismatic hybrid meshes are preferred in viscous flow simulation because they represent a good compromise between solution accuracy and ease of use.In a prismatic hybrid mesh,the near field of viscous walls is configured with layered prismatic elements to resolve high flow gradients normal to the walls,whereas the remaining domain is usually filled with an unstructured mesh.The generation of hybrid prismatic meshes involves several steps,i.e.,geometric processing,surface meshing,boundary layer meshing,tetrahedral meshing and mesh improving.To build an automatic pipeline for hybrid mesh generation,we need to solve a series of technical problems,which also makes the research of hybrid mesh generation becoming a hot topic in the field of numerical simulation.This study focuses on the preprocessing step for viscous flow simulation configured with complex geometries.An automatic pipeline for hybrid mesh generation is developed and several issues involved in this pipeline is studied carefully,and finally the following three contributions are achieved.Firstly,a new Boolean algorithm is proposed to handle the intersections and non-manifold edges involved in triangulated solids.This algorithm recasts Boolean operations as a boundary conforming tetrahedral meshing problem and the Boolean outputs are obtained through a top-down procedure.Different from those existing algorithms that merely maintain a conforming surface mesh,the new algorithm maintains a boundary conforming volume mesh at the same time of computing surface intersections.This volume mesh not only provides a background structure in helping the improvement of the efficiency of intersection computations,but also enables the development of a set of efficient and reliable flood-filling type procedures to extract the Boolean outputs.The efficiency and robustness of the proposed algorithm are investigated in further details,and various techniques are suggested to tackle these two issues accordingly.Secondly,a novel algorithm is proposed to create high quality sizing functions for surface mesh generation automatically.First,the tessellation of a CAD model is taken as the background mesh,in which an initial sizing function is defined by considering geometrical factors and user-specified parameters.Then,a convex nonlinear programming problem(NLP)is formulated to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions.The solvability and convexity of this NLP is proved rigorously,and an efficient numerical scheme that can balance solution quality and computing time is developed.The generation of prismatic layered meshes near the viscous wall is the key step in the procedure of hybrid mesh generation,and several issues involved in this step are still unresolved.A novel approach is proposed for viscous grid generation by the solution of a virtual heat conduction problem governed by the global Laplace equation.The gradient of the physical quantity at a point is taken as the marching direction at this point.In addition,the growth of the boundary layer elements is taken place in the solution space of the PDE.Compared to those traditional advancing front methods based on local geometric features,the possible intersections can be avoid naturally in this method.Besides,this new approach can ensure the smooth transition of marching directions and thereby lead to more desirable element shapes.Combined the above contributions with the surface mesher and tetrahedral mesher developed by our team,a preprocessing pipeline aimed at generating hybrid meshes in a completely automatic fashion is developed.This pipeline enables the generation of high quality hybrid meshes for complex geometries with only several user parameters,which effectively improved the efficiency of preprocessing procedure for the numerical simulation.The capability of the pipeline is demonstrated by meshing experiments on models with complex geometries.