Viscous fluid flow at all speeds: analysis and numerical simulation

In [43] a finite volume method for reliable simulations of inviscid fluid flows at high as well as low Mach numbers based on a preconditioning technique proposed by Guillard and Viozat [14] is presented. In this paper we describe an extension of the numerical scheme for computing solutions of the Euler and Navier-Stokes equations. At first we show the high resolution properties, accuracy and robustness of the finite volume scheme in the context of a wide range of complicated transonic and supersonic test cases whereby both inviscid and viscous flow fields are considered. Thereafter, the validity of the method in the low Mach number regime is proven by means of an asymptotic analysis as well as numerical simulations. Whereas in [43] the asymptotic analysis of the scheme is focused on the behaviour of the continuous and discrete pressure distribution for inviscid low speed simulations we prove both the physical sensible discrete pressure field for viscous low Mach number flows and the divergence free condition of the discrete velocity field in the limit of a vanishing Mach number with respect to the simulation of inviscid fluid flow.