MATRIX DISSIPATION FOR CENTRAL DIFFERENCE-SCHEMES WITH COMBUSTION

The effect of artificial viscosity is investigated for problems relate d to supersonic combustion, An implicit lower-upper symmetric Gauss-Se idel finite volume method is employed for solving the full, compressib le, two-dimensional averaged Navier-Stokes and species transport equat ions, For the right-hand side discretization central differences are u sed. Therefore some kind of artificial viscosity is necessary to reduc e oscillations near shock waves and to enable convergence to machine a ccuracy. In comparison to the standard second- and fourth-order scalar dissipation a matrix dissipation reduces the amount of artificial vis cosity by seating each equation individually. For the necessary absolu te flux Jacobian matrix a new decomposition is presented keeping the a dditional cost moderate. With an appropriate sensor the scheme also ge ts total variation diminishing properties. Calculations using differen t dissipation models are presented and advantages using a matrix dissi pation are shown.