Grid stabilization of high-order one-sided differencing II: Second-order wave equations

Authors:
Thomas Hagstrom;George Hagstrom
Affiliations:
Department of Mathematics, Southern Methodist University, P.O. Box 750156, Dallas, TX 75275-0156, United States;Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, United States
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

We demonstrate the stable boundary closure of difference methods of order up through 16 for the solution of wave equations in second order form. Our method combines the introduction of 1-2 judiciously placed subcell grid points near the boundary with minimal-stencil, one-sided difference operators of the same order as the interior scheme. The method is tested on a variety of problems including the scalar wave equation discretized on mapped grids and overlapping composite grids, as well as an integrable nonlinear system.