Stable Boundary Treatment for the Wave Equation on Second-Order Form

Authors:
Ken Mattsson;Frank Ham;Gianluca Iaccarino
Affiliations:
Department of Information Technology, Uppsala University, Uppsala, Sweden 751 05;Mechanical Engineering--Center for Integrated Turbulence Simulations, Stanford University, Stanford, USA;Mechanical Engineering--Flow Physics and Computation, Stanford University, Stanford, USA
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

A stable and accurate boundary treatment is derived for the second-order wave equation. The domain is discretized using narrow-diagonal summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension using high-order finite difference discretizations, and in three-dimensions using an unstructured finite volume discretization.