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

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• 作者：Tingting Li^a ; ^{ltt1120@mail.ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Chi-Wang Shu^b ; ^{shu@dam.brown.edu" class="auth_mail" title="E-mail the corresponding author} ; Mengping Zhang^a ; ^{mpzhang@ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：High order upwind-biased schemes ; Inverse Lax&ndash ; Wendroff procedure ; Extrapolation ; Stability ; GKS theory ; Eigenvalue analysis
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：299
• 期：Complete
• 页码：140-158
• 全文大小：608 K

文摘

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 Sundström) 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.