An explicit finite volume spatial marching method for reduced Navier-stokes equations

This paper develops a spatial marching method for high-speed flows based on a finite volume approach. The method employs the reduced Navier-Stokes equations and a pressure splitting in the streamwise direction based on the Vigneron strategy. For marching from an upstream station to one downstream the modified five-level Runge-Kutta integration scheme due to Jameson and Schmidt is used. In addition, for shock handling and for good convergence properties the method employs a matrix form of the artificial dissipation terms, which has been shown to improve the accuracy of predictions. To achieve a fast rate of convergence, a local time-stepping concept is used. The method retains the time derivative in the governing equations and the solution at every spatial station is obtained in an iterative manner. The developed method is validated against two test cases: (a) supersonic flow past a flat plate; and (b) hypersonic flow past a compression corner involving a strong viscous-inviscid interaction. The computed wall pressure and wall heat transfer coefficients exhibit good general agreement with previous computations by other investigators and with experiments.