Relationship Between Structured Mesh Quality and Error of Difference Scheme

The human resources and work time required for mesh generation are relatively high in the overall numerical simulation cycle of a flow field and represent a bottleneck in computational fluid dynamics applications. A large body of literature provides examples of calculations in which structured mesh quality has an impact on the results of difference scheme calculations, but few analyses are given of the mechanisms by which orthogonality and smoothness affect the errors. In this paper, the geometrically induced errors generated by the MUSCL and WENO difference schemes on non-uniform meshes were analysed, and it was found that there was no direct correlation between orthogonality and errors, and that the geometrical parameter that affects the errors was the deflection angle of the neighbouring grid points. The theoretical derivation proves that the error mainly originates from the governing equations and the difference schemes, and the improvement of the mesh quality can significantly reduce the geometrically induced error, but not completely eliminate it. In recent years, the algorithms were improved, and the discrete equivalent equations and their equivalent discretisation rule(DEER) and the unstructured finite difference methods were successively proposed. Through the simulations of free-stream preservation and linear-stream preservation cases, these improved algorithms can be used to obtain better computational results on poor quality meshes.