Artificial viscosity Q errors for strong shocks and moreaccurate shockfollowing methods
Abstract
The artificial viscosity (Q) method for von NeumannRichtmyer 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 Qinduced 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 nonuniform 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) shockfollowing method, which employs an artificial heatflux term (H) in addition to Q, and with the (nonQ) PPM method of Colella and Woodward. Both the (Q and H) and PPM methods (particularly when used with an adaptive shocktracking 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1985
 Bibcode:
 1985STIN...8617672N
 Keywords:

 Errors;
 Heat Flux;
 Shock Heating;
 Shock Wave Propagation;
 Simulation;
 Viscosity;
 Viscous Flow;
 Differential Equations;
 Hydrodynamics;
 Mathematical Models;
 Methodology;
 Procedures;
 Tensors;
 Fluid Mechanics and Heat Transfer