Stability analysis of WONDY (a hydrocode based on the artificial viscosity method of von Neumann and Richtmyer) for a special case of Maxwell’s law

Abstract

The artificial viscosity method of von Neumann and Richtmyer was originally designed and analyzed for stability in the case when the material was an ideal gas. Recently a hydrocode (WONDY) based on the von Neumann-Richtmyer scheme was used in calculating wave propagation problems in materials obeying a form of Maxwell’s material law; signs of an unstable difference scheme appeared. A stability analysis shows that the timestep restrictions required for stability in certain cases can be more stringent for material laws of the Maxwell type than they are for material laws of the ideal gas type.