基于非等距网格的紧致差分方法与经典差分方法的比较

Comparison between the Compact Finite Difference Method Based on Non-uniform Meshes and the Classical Finite Difference Method

采用泰勒展式系数匹配的方法构造出了非等距网格系统的紧致差分格式,并分析了其截断误差.与经典差分方法进行比较发现,紧致差分格式的基架要少于同价精度的经典差分格式,同价截断误差的紧致差分格式比经典差分格式计算误差小,非等距网格下紧致差分格式对网格的依赖性比经典差分格式强,网格对计算精度的影响较大.

Compact finite difference scheme （CFDS） based on non-uniform meshes is constructed by matching the Taylor series coefficient expansion, and its truncation errors are analyzed. Compared with classical finite difference scheme （FDS）, the CFDS needs less pedestal on the same order precision and its same order truncation error is smaller than that of the FDS, the selecting of grid system greatly influences on computing accuracy and the CFDS has stronger dependence on the grid system based on non-uniform meshes.