Research On Polyhedral Mesh Quality Based On Finite Volumn Method

In recent years,with the diversification of numerical simulation application scenarios,how to generate and improve polyhedral meshes has received more and more attention in Computational Fluid Dynamics(CFD)based on the Finite Volume Method(FVM).First of all,it does still need further study on measuring the quality of polyhedral meshes.At the same time,it is a great challenge to optimize the quality of polyhedral meshes.In this thesis,the quality measurement and optimization method of polyhedral meshes are studied based on the FVM,and the main work is as follows:Firstly,based on FVM,the truncation errors are analyzed theoretically on different types of meshes and different flow regimes.From theoretical analysis,it can be seen that the truncation error is in inverse ratio to the mesh-to-flow alignment degree.Accordingly,the mesh quality measurement is proposed,which measures the mesh quality by the angle between the velocity vector and the mesh face normal: the larger the angle,the better the quality of the mesh,and the smaller the corresponding computational truncation error.For vortex and laminar flow,the computational error ratios based on hexagonal and quadrilateral meshes are computed.The results show that the error ratio is about 1.155 in laminar flow simulations,while it is less than 1 in vortex simulations when the mesh-toflow alignment degree is in(0,83).Therefore,the experimental results are consistent with the theoretical analysis.Secondly,the mesh interfaces transforming method is proposed,which improves the mesh quality by moving the mesh interfaces.The experimental results show that the mesh interfaces transforming method,which can achieve 6 times the non-orthogonality of the Laplacian smoothing method,usually gets better non-uniformity and skewness than the Laplacian smoothing method.Furthermore,it can yield lower computing costs and faster convergence rate,The proposed mesh quality measurement provides new criteria for mesh selection.The mesh interfaces transforming method gives a new methodology to improve the mesh quality.These results provide a new perspective for the study of polyhedral mesh quality measure and optimization methods,which will be useful to impetus the theoretical analysis and engineering application of polyhedral meshes.