Use of artificial viscosity in multidimensional fluid dynamic calculations

Abstract

The von Neumann-Richtmyer concept of artificial viscosity that is used in calculating the propagation of shocks was formulated in one space-dimension. A generalization of the method for two and for three space-dimensions is presented here. The basic objectives were to find the one-dimensional equivalent of shock compression that avoided geometric convergence effects and to determine a characteristic grid length. A description is given of a linear viscosity for damping the spurious oscillations that arise when the quadratic von Neumann-Richtmyer artificial viscosity is used. The linear viscosity minimizes the smearing of the shock front. Unwanted distortions that can occur in multidimensional grids are discussed. Results in two and three dimensions are given for the Navier-Stokes-type viscosity developed to damp these distortions.