Density diffusion in low Mach number flows

Abstract

Abstract In the realm of compressible viscous flow modelling, we briefly revisit the debate on a possible inconsistency of the Navier-Stokes (NS) equations. Then, we recall a recent proposal from the literature, put forward by M. Svärd. One of its features is the mass diffusive term in the continuity equation. The presence of density diffusion in the Svärd model reduces dispersive numerical errors when simple centred 2nd order, numerical diffusion free, spatial schemes are used, as confirmed in the simulations of a doubly-periodic shear layer at Ma = 0.05 and Re = 104. Further reduction of the dispersive errors at the spatial discretisation level is possible by more sophisticated approximation techniques.