A first-order hyperbolic system of governing equations for miscible and viscous compressible fluids

In this paper we introduce a reformulation of the compressible multicomponent Navier-Stokes equations that govern the behaviour of mixtures of miscible gases. The resulting equation set is a first-order hyperbolic system containing stiff source terms, which recovers the conventional parabolic theory of viscosity, conduction and diffusion as a first-order approximation in the relaxation limit. An important advantage of this approach versus other first-order reformulations of the Navier-Stokes equations is that the wave speeds remain finite as some relaxation parameter tends to zero. The complete system of equations is presented in one-dimension for binary mixtures of viscous, heat conducting gases.