A POSTERIORI METHODS WITH AUTOMATIC DISSIPATION ADJUSTMENT FOR THE SIMULATION OF COMPRESSIBLE FLOWS

Abstract

In this work, a generalized framework for the numerical computations of the compressible Euler and Navier–Stokes equations is presented in order to increase the accuracy of any numerical scheme that uses a numerical flux that can be rewritten as a central term plus some dissipation term. The key idea is to regulate the numerical dissipation introduced by the scheme in real-time according to some estimate of the high-frequency content in the flow. This technique is called adaptive dissipation, and has been applied successfully to the calculation of incompressible turbulent flows. In the present case, and due to the compressibility effects, the methodology may present some stability problems, in order to remedy this behavior, we couple the adaptive dissipation methodology with an a posteriori procedure that guarantees that the solution remains physical at all times. We validate the proposed methodology with a finite volume and a finite difference scheme, with some oneand three-dimensional test cases, obtaining solutions that are physical and in really good agreement with the ones that can be found in the literature.