Errors in Numerical Solutions of Spherically Symmetric Shock Physics Problems
Errors in Numerical Solutions of Spherically Symmetric Shock Physics Problems
复制标题
球对称激波物理问题数值解中的误差
DOI：
10.1090/conm/371/06853
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Xiaolin Li
中科院分区：
文献类型：
--
作者：
J. Glimm;J. Grove;Yunghee Kang;Taewon Lee;Xiaolin Li
摘要：作者为激波物理模拟寻找稳健和可理解的误差模型。本文的目的是探讨球流在激波干扰问题数值解误差分析中引入的复杂性。与平面波的情况不同，球面波在相互作用之间的强度不是恒定的，波间的解也不是分段恒定的。然而，简单的幂定律预测解对半径的依赖性。作者发现，同样的幂定律预测了误差的演变，因为一旦形成误差，就会按照支配解结构(即波)本身的相同规律传播。他们基于对单个相互作用的分析和一个多路径散射公式来分析复合波相互作用问题中的误差，以结合通过单个相互作用传播的误差的影响。他们改进了之前为识别和分析平面(1D)冲击物理模拟中的波强和位置而引入的波滤器。现在，该滤波器必须适用于波与波之间状态不恒定的情况。与物理解相比，数值解在紧邻数值波的狭窄区域内是近似恒定的。出于这个原因，平面一维滤波器提供了足够的精度，并且无需更改即可使用。然而，当他们考虑在二维圆柱几何(r，z)或三维矩形几何(x，y，z)中解决相同问题时，还考虑微扰球面问题的解(例如，球面Richtmyer-Meshkov不稳定性问题)，将需要更高维的波滤波器。本文针对这一模式识别问题提出了一种解决方案。(表5，图8，参考文献8)
Abstract : 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.)