A Cartesian Embedded Boundary Method for Hyperbolic Conservation Laws (Communications in Computational Physics, 2007)
We develop an embedded boundary finite difference technique for solvingthe compressible two- or three-dimensional Euler equations in complex geometries ona 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 computedon a body fitted grid. Furthermore, we discuss the implementation of the method forthin geometries, and show computed examples of transonic flow past an airfoil.