The Cartesian grid method has been investigated for the 2D compressible Euler equations. We impose wall boundary conditions by a simplified ghost point treatment for compressible inviscid flows with immersed boundaries. In the simplified ghost point treatment we assume the solid boundary lie in the middle between two grid points in the y direction. Symmetry conditions are used to determine density, pressure, wall tangential, and wall normal velocity components at the ghost points. A first order

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... node-centered finite volume formulation has been used to calculate compressible flows. The order of this formulation is increased by employing MUSCL with the minmod limiter. The code is tested for external flows over a circular arc airfoil. We compare our results for the simplified ghost point treatment with a standard body-fitted grid method. We obtain similar results for the Cartesian grid method as for the standard body-fitted grid method for external flows.