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

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. (C) 2015 Elsevier B.V. All rights reserved.