On the Use of Nonlinear Filtering, Artificial Viscosity, and Artificial Heat Transfer for Strong Shock Computations

Abstract

A new artificial viscosity (Q) model, based on physical conservation corrections for momentum, and a new artificial heat transfer (H) formulation are developed for the analysis of one-dimensional compressible fluid transients in plane, cylindrical, and spherical geometries. The accuracy of these formulations is verified against various benchmark shock tube problems. A Q-induced geometric error for cylindrical and spherical geometry is defined and the benefits of the Q formulation presented are demonstrated. It is also shown that these formulations can control the total variation of the solution and have superior shock-capturing capabilities. Comparisons are made with the original Q formulations of J. von Neumann and R. D. Richtmyer (1950, J. Appl. Phys.21, 232), W. F. Noh's Q&H shock-following method (1987, J. Comput. Phys.72, 78), and the piecewise-parabolic method of P. Colella and P. R. Woodward (1984, J. Comput. Phys.54, 174). The comparisons demonstrate the advantages of the new method. Numerical examples for more realistic equations of state which show the robustness of the method are also presented.