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

  • Ken MattssonEmail author
  • Frank Ham
  • Gianluca Iaccarino


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.


High-order finite difference methods Unstructured finite volume method Wave equation Numerical stability Second derivatives Boundary conditions Complex geometries 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden
  2. 2.Mechanical Engineering—Center for Integrated Turbulence SimulationsStanford UniversityStanfordUSA
  3. 3.Mechanical Engineering—Flow Physics and ComputationStanford UniversityStanfordUSA

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