Departments of Mathematics, Computational and Applied Mathematics,

We present a generalized discontinuous Galerkin method for a mul-ticomponent compressible barotropic Navier-Stokes system of equations. The system presented has a functional viscosity ν which depends on the pressure p = p(ρ, µi) of the flow, with the density ρ and the local con-centration µi. High order Runge-Kutta time discretization techniques are employed, and different methods of dealing with arbitrary coupled boundary conditions are discussed. Analysis of the energy consistency of the scheme is performed in addition to inspection of the relative error of the solution compared to exact analytic test cases. Finally several exam-ples, comparisons, generalizations and physical applications are presented