Instability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes

摘要

The stability characteristics of various compact fourth- and sixth-order spatialoperators are assessed using the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semi-discrete Initial Boundary Value Problem (IBVP). These results are then generalized to the fully discrete case using a recently developed theory of Kreiss. In all cases, favorable comparisons are obtained between G-K-S theory, eigenvalue determination, and numerical simulation. The conventional definition of stability is then sharpened to include only those spatial discretizations that are asymptotically stable (bounded, Left Half-Plane eigenvalues). It is shown that many of the higher-order schemes which are G-K-S stable are not