Commun. Comput. Phys., 2 (2007), pp. 1199-1219.

A Cartesian Embedded Boundary Method for Hyperbolic Conservation Laws

Björn Sjögreen 1*, N. Anders Petersson 1

1 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Received 4 January 2007; Accepted (in revised version) 11 April 2007
Available online 2 August 2007


We develop an embedded boundary finite difference technique for solving the compressible two- or three-dimensional Euler equations in complex geometries on a Cartesian grid. The method is second order accurate with an explicit time step determined by the grid size away from the boundary. Slope limiters are used on the embedded boundary to avoid non-physical oscillations near shock waves. We show computed examples of supersonic flow past a cylinder and compare with results computed on a body fitted grid. Furthermore, we discuss the implementation of the method for thin geometries, and show computed examples of transonic flow past an airfoil.

AMS subject classifications: 65M06, 65M50, 76J20

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Key words: Embedded boundary, hyperbolic conservation law, finite difference scheme, shock wave.

*Corresponding author.
Email: (B. Sjögreen), (N. A. Petersson)

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