SPH方法中的Riemann解与人工粘性

本文描述了光滑粒子动力学方法的人工粘性和Riemann解方法,分析了Godunov方法与传统人工粘性方法的耗散项．给定一种人工粘性,总可以找到一种相应的Riemann解法器,使得它们的耗散项在形式上几乎相同．本文利用各种近似Riemann解构造了相应的新的人工粘性．这些新的粘性,无需人工调节粘性系数．本文完成了多个数值试验,比较了使用传统人工粘性方法与Riemann解方法的不同．采用新的人工粘性,辅助热通量粘性,可以获得令人满意的计算结果．

RIEMANN SOLVER AND ARTIFICIAL VISCOSITY IN SPH

This paper describes the artificial viscosity and Godunov methods in Smoothed Particle Hydrodynamics (SPH) and analyzes the dissipative term which appears in traditional SPH and Godunov method. A traditional artificial viscosity can be mapped to a Riemann solver to keep the dissipative term almost the same, although not equivalence. Due to turning off the viscosity in rarefaction wave region the artificial viscosity method is more accurate than Godunov method. Utilizing some different approximate Riemann solvers directly, we construct some new artificial viscosities correspondingly without adjusting viscosity coefficients. With the help of heat conduction viscosity, these new viscosities give some very good numerical results in numerical experiments.