TIME-STABLE BOUNDARY-CONDITIONS FOR FINITE-DIFFERENCE SCHEMES SOLVING HYPERBOLIC SYSTEMS - METHODOLOGY AND APPLICATION TO HIGH-ORDER COMPACT SCHEMES

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative. A ''simultaneous approximation term'' is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach. (C) 1994 Academic Press, Inc.