Mh. Carpenter et al., TIME-STABLE BOUNDARY-CONDITIONS FOR FINITE-DIFFERENCE SCHEMES SOLVINGHYPERBOLIC SYSTEMS - METHODOLOGY AND APPLICATION TO HIGH-ORDER COMPACT SCHEMES, Journal of computational physics, 111(2), 1994, pp. 220-236
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.