A consistent artificial diffusivity model for capturing discontinuities in compressible flows using central spatial discretization

We present a novel computational model for simulation of compressible flows involving shocks and contact discontinuities using an artificial diffusivity approach. Owing to their non-dissipative nature and secondary conservation properties, second order central operators have been shown to be very accurate for simulation of turbulent flows and acoustics. Committing to second order central spatial operations, we control their large dispersion errors by augmenting the mass, momentum and total energy equations with artificial mass diffusivity, artificial shear/bulk viscosities and artificial thermal conductivity, respectively. We show that the presence of artificial mass diffusivity must be consistently accounted for by additional terms in the momentum and total energy equations and compatibility conditions must be met when discretely computing these terms. Next, unlike previous phenomenological localization strategies, inspired by analysis of second order TVD schemes, we present a novel approach for localizing the artificial diffusivity terms. The performance of our proposed computational model is first assessed using canonical 1D tests. Finally, we present simulation results from realistic problems involving shock-boundary layer interactions in a compression corner geometry.