关于非均匀网格高精度格式的误差分析方法

Error analysis of high order schemes on non-uniform grids

以三次样条重构有限体积方法为例,研究非均匀网格上截断误差的分析方法。通过推导得到了分析非均匀网格上截断误差的基本准则,即在非均匀网格的截断误差分析中,要保证不显式或者隐含地改变数值方法对应的模板点——当不满足这一准则时,误差分析会得到不自洽的结果;而满足这一准则时,可保证分析结果的正确性。利用正确的误差分析结果,可发展进一步提高计算精度的措施。据此发展了扩散项在非均匀网格上达到三阶精度计算方法,从而可以使对流项和扩散项的计算达到一致三阶精度。

The derivation of truncation error on non-uniform grid for cubic spline reconstruction in finite volume framework is analyzed in this paper.The basic rule for the derivation of truncation error on non-uni-form grid is proposed which is that all derivations in the truncation error analysis should base on the same stencil.If this rule is not satisfied,the truncation error will not be self-consistent.Furthermore,the third-order discretization of the diffusion terms is obtained based on the correct truncation error analysis which makes both the convection and diffusion terms to achieve consistent third-order accuracy.