Artificial viscosity Q errors for strong shocks and more-accurate shock-following methods

The artificial viscosity (Q) method for von Neumann-Richtmyer is a tremendously useful numerical technique for following shocks wherever and whenever they appear in the flow. We show that it must be used with some caution, however, as serious Q-induced errors (approx. =100%) can occur in some strong shock calculations. We investigate three types of Q errors: (1) Excess Q heating, of which there are two types: (a) excess Wall Heating on shock formation and (b) Shockless Q Heating; (2) Q errors when shocks are propagated over a non-uniform mesh; and (3) Q errors in propagating shocks in spherical geometry. As a basis of comparison, we use as our standard the Lagrangian formulation with Q = C0 sup 2 rho L sup 2 (u sub x) sup 2. This standard Q is compared with Noh's (Q and H) shock-following method, which employs an artificial heat-flux term (H) in addition to Q, and with the (non-Q) PPM method of Colella and Woodward. Both the (Q and H) and PPM methods (particularly when used with an adaptive shock-tracking mesh) give superior results for our test problems. In spherical geometry, Schulz's tensor Q formulation of the hydrodynamic equations proves to be most accurate.