Numerical Solution of the Linearized Euler Equations Using High Order Finite Difference Operators with the Summation by Parts Property

Stefan Johansson

October 2002

Abstract:

We have used high order finite difference methods with the summation by parts property (SBP) on the 1D linearized Euler equations. The boundary conditions are imposed with both the projection method and the simultaneous approximation term method (SAT) for comparison. The formal fourth order of accuracy of the high order SBP operator was verified with both the projection method and the SAT method. Some relatively large errors were observed at the artificial boundaries and further investigations are needed to improve the non-reflecting boundary conditions.

Note: Updated version, March 2003, available at http://www.it.uu.se/research/publications/reports/2002-034/2002-034-updated (PDF and Postscript)

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