Research On Unwarp Algorithm For Polyhedral Mesh Based On Discrete Laplacian Operator

Polyhedral and polygonal meshes have been around for nearly a decade in the field of Computational Fluid Dynamics(CFD),which overcomes some of the drawbacks of traditional meshes,including the more adjacent cells that make gradient calculations and local flow conditions more accurate,and the same computational domain requires fewer grids to reduce the amount of computation.Compared with tetrahedral mesh,polyhedral mesh reduces the influence of mesh deformation on calculation accuracy.Due to the small number of tools that can generate and optimize the polyhedron grid directly,the details of related documents are also lacking,resulting in the inconvenience of the polyhedral grid application.Based on the achievements in the computational geometry and graphics in recent years,this paper proposes a suppression algorithm for warpage of polygons in polyhedral mesh.In this model,discrete Laplacian operator is constructed on 3d polygon and a quadratic functional energy that embodies the global warping in the grid is minimized.L-BFGS(Limited-memory Broyden-Fletcher-Goldfarb-Shanno)optimization algorithm is applied to solve the extremum of functional energy.The realization of program code is based on C language and developed on Code_Saturne open source general computational fluid software platform,which verifies the warpage problem in different grid types,and the flow calculation results of the U bend tube are obtained to show the impact of the model proposed.The results show that the model proposed in this paper can effectively suppress the warpage of the non-structural mesh with arbitrary number of sides.