TimeStable Boundary Conditions for FiniteDifference Schemes Solving Hyperbolic Systems: Methodology and Application to HighOrder Compact Schemes
Abstract
We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Padélike) highorder finitedifference schemes for hyperbolic systems. First a proper summationbyparts formula is found for the approximate derivative, A "simultaneous approximation term" is then introduced to treat the boundary conditions. This procedure leads to timestable schemes even in the system case. An explicit construction of the fourthorder compact case is given. Numerical studies are presented to verify the efficacy of the approach.
 Publication:

Journal of Computational Physics
 Pub Date:
 April 1994
 DOI:
 10.1006/jcph.1994.1057
 Bibcode:
 1994JCoPh.111..220C
 Keywords:

 Boundary Conditions;
 Computational Fluid Dynamics;
 Finite Difference Theory;
 Hyperbolic Functions;
 Numerical Integration;
 Accuracy;
 Divergence;
 Matrices (Mathematics);
 Scalars;
 Fluid Mechanics and Heat Transfer