Numerical treatment of interfaces for second-order wave equations

Details Numerical treatment of interfaces for second-order wave equations Numerical treatment of interfaces for second-order wave equations

2011-12-13

arxiv.org/abs/1112.3039v1

Physics

Computational Physics

17 pages, 12 figures

Scientific paper

In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. In the spirit of the Simultaneous Approximation Term (SAT) schemes introduced in \cite{Carpenter1999341}, information is passed among grids using the values of the fields only at the contact points between them (actually, in our case, just the values of the field corresponding to the time derivative of the field). The scheme seems to be as accurate as the space and time discretizations used for the corresponding derivatives. The semi-discrete approximation preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge-Kutta method. This is crucial for, otherwise, the methods will be impractical given the severe restrictions its stiff parts would put on totally explicit integrators.

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