Stability analysis of the inverse Lax-Wendroff boundary treatment for high order upwind-biased finite difference schemes

作者：Li, Tingting; Shu, Chi-Wang^*; Zhang, Mengping

来源：Journal of Computational and Applied Mathematics, 2016, 299: 140-158.

DOI：10.1016/j.cam.2015.11.038

• High order upwind-biased schemes
• Inverse Lax-Wendroff procedure
• Extrapolation
• Stability
• GKS theory
• Eigenvalue analysis

In this paper, we consider linear stability issues for one-dimensional hyperbolic conservation laws using a class of conservative high order upwind-biased finite difference schemes, which is a prototype for the weighted essentially non-oscillatory (WENO) schemes, for initial-boundary value problems (IBVP). The inflow boundary is treated by the so-called inverse Lax-Wendroff (ILW) or simplified inverse Lax-Wendroff (SILW) procedure, and the outflow boundary is treated by the classical high order extrapolation. A third order total variation diminishing (TVD) Runge-Kutta time discretization is used in the fully discrete case. Both GKS (Gustafsson, Kreiss and Sundstrom) and eigenvalue analyses are performed for both semi-discrete and fully discrete schemes. The two different analysis techniques yield consistent results. Numerical tests are performed to demonstrate the stability results predicted by the analysis.

• 出版日期2016-6
• 单位中国科学技术大学