Technical Report 2011-019

A Weak Boundary Procedure for High Order Finite Difference Approximations of Hyperbolic Problems

Qaisar Abbas and Jan Nordström

September 2011

We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.

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