Simplified of time averaged Navier-Stokes equations and Reynold's stress equations for an implicit sweep

Abstract

Abstract: This paper presents an improved method of upwind the Euler part of the uxes with the Reynolds-stress closure model. This new method takes account the anisotropic nature of the Reynolds-stresses. Resulting eigenvalues show effect of the anisotropy. Because the characteristic variables and the right eigenvector matrix are relatively complex, a simplified diagonalization is introduced.

Main result: Possible equations for upwinding.