A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain (Communications in Computational Physics, 2014)
A new weak boundary procedure for hyperbolic problems is presented. Weconsider high order finite difference operators of summation-by-parts form with weakboundary conditions and generalize that technique. The new boundary procedure isapplied near boundaries in an extended domain where data is known. We show howto raise the order of accuracy of the scheme, how to modify the spectrum of the resultingoperator and how to construct non-reflecting properties at the boundaries. Thenew boundary procedure is cheap, easy to implement and suitable for all numericalmethods, not only finite difference methods, that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.