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An algorithm for unsteady viscous flows at all speeds. (English) Zbl 1003.76057

Summary: We present an algorithm for simulation of unsteady viscous stratified compressible flows, which remains valid at all speeds. The method is second-order accurate in both space and time, and is independent of Mach number. In order to remove the stiffness of numerical problem due to large disparity between flow speed and acoustic wave speed at low Mach number, we propose an approximate Newton method based on artificial compressibility. Additionally, a modified advection upstream splitting method (AUSM+) is used, which permits accurate computations of both compressible and incompressible flows. We give a detailed comparison with other approximate Newton methods described in the literature. Furthermore, through computations of various benchmark test cases it is shown that the accuracy of algorithm does not depend on Mach number.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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