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 roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) 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. Carpenter, Mark H. and Gottlieb, David and Abarbanel, Saul Unspecified Center NAS1-19480; NAS1-18605; RTOP 505-90-52-01...