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

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