Analysis and Design of Numerical Schemes for Gas Dynamics 2 Arti cial Di usion and Discrete Shock Structure

The e ect of arti cial di usion on discrete shock structures is examined for a family of schemes which includes scalar di usion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the di usive ux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP scheme in which the coe cients of the pressure di erences is fully determined by the coe cient of convective di usion. It is also shown how both the characteristic and CUSP schemes can be modi ed to preserve constant stagnation enthalpy in steady ow, leading to four variants, the E and H-characteristic schemes, and the E and H-CUSP schemes. Numerical results are presented which con rm the properties of these schemes.