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Adaptive Cartesian grid methods for representing geometry in inviscid compressible flow

In this paper we describe a Cartesian grid algorithm for modeling time-dependent compressible flow in complex geometry. In this approach problem geometry is treated as an interface embedded in a regular Cartesian mesh. The discretization near the embedded boundary is based on a volume-of-fluid approach with a redistribution procedure to avoid time-step restrictions arising from small cells where the boundary intersects the mesh. The algorithm is coupled to an unsplit second-order Godunov algorithm and is fully conservative, maintaining conservation at the boundary. The Godunov/Cartesian grid integration scheme is coupled to a local adaptive mesh refinement algorithm that selectively refines regions of the computational grid to achieve a desired level of accuracy. Examples showing the results of the combined Cartesian grid/local refinement algorithm for both two- and three-dimensional flows are presented.