关键词: 有限差分法, 高阶WENO格式, 几何诱导误差, 边界近似模型误差, 双曲型方程

Abstract: This paper compares the numerical results obtained from simulation of moving shock discontinuity, contact discontinuity, uniform flow in the curvilinear coordinate system and shock regular reflection in the first-order upwind scheme and the fifth-order WENO schemes. The shock and contact discontinuities simulated in the WENO schemes exhibit more pronounced non-physical fluctuations and more complicated flow field structures while changing from the initial discontinuity to the numerical transition region than the results in the first-order upwind scheme. Furthermore, the geometrically induced errors and boundary approximation model errors caused by coordinate transformations are significantly larger than those in the first-order upwind scheme. Numerical and theoretical analyses of the phenomena above conclude that higher-order WENO schemes run the risk of magnifying errors in the results under certain computational conditions. Finally, inspired by recently published articles, this paper discusses the contradiction between the current spatial multi-point construction method in high-order schemes and the characteristic line theory of hyperbolic equations.

Key words: finite difference methods, high-order WENO schemes, geometrically induced errors, boundary approximation model errors, hyperbolic governing equations