Matrix dissipation for central difference schemes with combustion

Abstract

The effect of artificial viscosity is investigated for problems related to supersonic combustion. An implicit lower-upper symmetric Gauss-Seidel finite volume method is employed for solving the full, compressible, two-dimensional averaged Navier-Stokes and species transport equations. For the right-hand side discretization central differences are used. Therefore some kind of artificial viscosity is necessary to reduce oscillations near shock waves and to enable convergence to machine accuracy. In comparison to the standard second- and fourth-order scalar dissipation a matrix dissipation reduces the amount of artificial viscosity by scaling each equation individually. For the necessary absolute flux Jacobian matrix a new decomposition is presented keeping the additional cost moderate. With an appropriate sensor the scheme also gets total variation diminishing properties. Calculations using different dissipation models are presented and advantages using a matrix dissipation are shown.