Abstract

In this talk, we will study the property of finite difference (FD) weighted essentially non-oscillatory (WENO) schemes on curvilinear meshes. To maintain the free-stream solution of Euler equation exactly, we will look at the alternative formulation of the FD WENO schemes, in which WENO interpolation of the solution and its derivatives are used to directly construct the numerical flux, instead of the usual practice of reconstructing the flux functions. Theoretical derivation and numerical results show that the FD WENO schemes based on the alternative flux formulation can preserve free-stream and vortex solutions on generalized coordinate systems, hence giving much better performance than the standard FD WENO schemes for such problems. Furthermore, we extend the method to solve the ideal magnetohydrodynamics equations and the shallow water equations, such that it can preserve the free-stream condition and well-balanced property on curvilinear meshes, respectively.

个人简介：蒋琰，中国科学技术大学特任研究员。2015 年于中国科学技术大学取得博士学位，2015年至2018年在美国密歇根州立大学从事博士后 工作。主要研究方向为高精度偏微分方程数值方法的理论与应用。在 SIAM Journal on Scientific Computing 和 Journal of Computational Physics 等期刊发表论文十余篇。