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Development of an Upwind Algorithm at Subsonic Regions in the Solution of PNS Equations

In this paper an upwind algorithm based on Roeʹs scheme is presented for solution of PNS equations. Non iterative-implicit method using finite volume technique is used. The main advantage of this approach, in comparison with similar upwind methods, is reduction of oscillations around sonic line. This advantage causes the present method to be able to analyze supersonic flows with free stream Mach number near to one, where similar upwind methods normally fail. Some two dimensional/ axisymmetric test cases have been computed to validate the present method. These cases are: Hypersonic flow over a 15-degree compression ramp, two-dimensional supersonic flow over a flat plate and axisymmetric supersonic flow over a tangentogive. The results are compared with the results of other numerical schemes, such as Beam and Warming scheme .