Numerical study of two models for viscous compressible fluid flows

Abstract

Our aim is to evaluate the modelling capability of a recently proposed (Eulerian) model for viscous and heat conducting compressible fluids. The new model differs from the Navier-Stokes in the structure of the diffusive terms. Most notably, it includes a mass diffusive mechanism. Despite the lack of well-posedness theory, one has to recognize that the standard Navier-Stokes equations are known to give reasonably accurate results for numerous standard problems. Hence, the new model can not deviate too much from the Navier-Stokes equations for such cases, is it to be an accurate model. The purpose of the paper is to compare the new model with Navier-Stokes and determine an unknown model parameter (α) in the new model such that the best matches are obtained. Using a high-order discontinuous Galerkin scheme, with careful implementations of the boundary conditions, we perform accurate simulations of the two models for a suite of test cases. For the grid converged results, we have, for each problem, compared the two models with respect to a number of measures such as cL, cD, cM, skin friction coefficients, pressure coefficients and Mach number or pressure isolines. The numerical results reveal a remarkable sameness (the differences are typically 1%) of both models when α=1.