Adaptive grid computation for inviscid compressible flows using a pressure correction method

Effort has been devoted to extending a pressure correction based incompressible flow algorithm developed earlier to calculate compressible flows. The resulting algorithm represents a substantial generalization of the original algorithm, retaining the same basic structure (curvilinear coordinates, staggered grid, pressure correction method, no artificial smoothing terms) and capabilities of the original scheme while adding the new capabilities. With the inclusion of the density variation effects, the pressure correction equation now becomes a convection-diffusion type of transport equation, instead of being a diffusion type of equation as it is for incompressible cases. The convection effects are dominant for high Mach number flow, and can affect the stability of the low Mach number flow computation. Appropriate numerical treatments are necessary to account for this change of characteristics of the pressure correction equation. The modified pressure correction equation also requires a change of the boundary conditions for pressure between subsonic and supersonic flows. By combining the revised algorithm and an adaptive grid procedure developed earlier, accurate inviscid flow solutions over a wide range of Mach numbers can now be successfully obtained. Several different flow problems, ranging from subsonic and transonic to hypersonic, have been computed to demonstrate the performance of the new algorithm.