On the artificial viscosity in 1D spherical geometry
W. P. Crowley · 1987
An artificial viscosity formulation based on the conservation equations for viscous compressible hydrodynamics is considered. The method uses tensor analysis to properly transform Richtmyer and von Neumann's artificial viscosity to non-planar geometries. It will be shown that the naive replacement of p by p+q in the Cartesian equations leads to poor results when these equations are used in spherical geometries. In section 2 the viscous equations of motion for 1D spherical geometry are discussed. Section 3 the difference equations for momentum and energy are derived. In sections 4 and 5 the two viscosity coefficients, ..mu.. and lambda, are discussed. In section 6 describes computational results. Appendix A contains the tensor formulation and Appendix B shows the equations for cylindrical geometry. 4 refs., 7 figs.