Volume 2, Issue 6
A Cartesian Embedded Boundary Method for Hyperbolic Conservation Laws

B. Sjögreen & N. A. Petersson

DOI:

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

Published online: 2007-02

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  • Abstract

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.

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@Article{CiCP-2-1199, author = {}, title = {A Cartesian Embedded Boundary Method for Hyperbolic Conservation Laws}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {6}, pages = {1199--1219}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7946.html} }
TY - JOUR T1 - A Cartesian Embedded Boundary Method for Hyperbolic Conservation Laws JO - Communications in Computational Physics VL - 6 SP - 1199 EP - 1219 PY - 2007 DA - 2007/02 SN - 2 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/cicp/7946.html KW - AB -

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.

B. Sjögreen & N. A. Petersson. (2020). A Cartesian Embedded Boundary Method for Hyperbolic Conservation Laws. Communications in Computational Physics. 2 (6). 1199-1219. doi:
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