Errors in Numerical Solutions of Spherically Symmetric Shock Physics Problems

摘要

The authors seek robust and understandable error models for shock physics simulations. The purpose of this paper is to explore complications introduced by spherical flow in the analysis of errors in the numerical solution of shock interaction problems. In contrast to the case of planar waves, the spherical waves are not constant in strength between interactions and the solution is not piecewise constant between waves. Nevertheless, simple power laws predict the dependence of the solution on the radius. The authors find that the same power laws predict the evolution of the error, as the error once formed propagates according to the same laws that govern the solution structures (i.e., the waves) themselves. They analyze errors in composite wave interaction problems based on the analysis of single interactions and a multi-path scattering formula to combine the effects of errors propagating through the individual interactions. They refine the wave filters they have previously introduced for the identification and analysis of wave strength and position in planar (1D) shock physics simulations. The filter now must be applicable to the case of non-constant states between waves. The numerical solutions, in contrast to the physical solutions, are approximately constant in a narrow region immediately adjacent to the numerical waves. For this reason, the planar one- dimensional wave filters provide sufficient accuracy and are used without change. However, as they contemplate the solution of the same problem in a two- dimensional cylindrical geometry (r, z) or three-dimensional rectangular geometry (x, y, z), and also contemplate the solutions of perturbed spherical problems (e.g., the spherical Richtmyer-Meshkov instability problem), there will be a need for higher dimensional wave filters. This paper offers a solution to this pattern recognition problem. (5 tables, 8 figures, 8 refs.).