Abstract
Abstract Parabolized Navier-Stokes (PNS) solution techniques for high speed compressible flow involve marching in a “time like” spatial coordinate but have been observed in practice to be sensitive to flow conditions and require stabilization by numerical dissipation techniques. In this study we develop an eigenvalue analysis for shock stability. Using the algebraic symbolic manipulator MACSYMA, an explicit closed-form solution for the shock system eigenvalues is developed. This is then applied on the evolving shock contour to determine the stability limit on the PNS stepsize. Numerical experiments confirm the validity of the approach and demonstrate that the approach can be implemented explicitly to yield an adaptive stepsize algorithm and thereby a more robust PNS scheme.
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