Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem
Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem
复制标题
多媒体黎曼问题各种幻影流体方法的精度和守恒误差
DOI：
10.1016/j.jcp.2011.03.021
复制
发表时间：
2011-06
影响因子：
4.1
通讯作者：
Liu, Tiegang
中科院分区：
文献类型：
--
作者：
Xu, Liang;Liu, Tiegang
自Fedkiw等人于1999年提出（原始的）虚流体方法（OGFM）以来[5]，随后又发展了一系列基于GFM的方法，如气-水版本GFM（GWGFM）、修改的GFM（MGFM）和真实的GFM（RGFM）。然而，对各种几何模型的精度和守恒误差还没有进行系统的分析。在本文中，我们开发了一种技术，严格分析这些不同的GFM的精度和守恒误差时，适用于多介质黎曼问题的一般状态方程（EOS）。通过分析和比较每个GFM提供的界面状态与原始多介质Riemann问题的精确解，我们表明，在与原始多介质Riemann问题的精确解相比的意义上，MGFM和RGFM的界面处理的精度可以达到“三阶精度”，而当界面方法实际上接近平衡时，OGFM和GWGFM的精度最多为“一阶精度”。对于局部守恒误差也得到了类似的结论。通过一种特殊的试验方法，从数值的角度验证了这些理论结论.
Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas–water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve “third-order accuracy” in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most “first-order accuracy” for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint.
登录
查看更多内容
改进幻影流体法的最优误差估计
影响因子：
3.7
作者：
Xu, Liang;Liu, Tiegang
通讯作者：
Liu, Tiegang
影响因子：
4.1
作者：
S. O. Unverdi;G. Tryggvason
通讯作者：
S. O. Unverdi;G. Tryggvason
DOI：
10.1142/9781860949524_0027
发表时间：
2002-12
期刊：
--
影响因子：
--
作者：
T. Liu;K. C. Hung;B. Khoo
通讯作者：
T. Liu;K. C. Hung;B. Khoo
DOI：
--
发表时间：
2002
期刊：
--
影响因子：
--
作者：
D. Nguyen
通讯作者：
D. Nguyen
影响因子：
4.1
作者：
Ronald Fedkiw;A. Marquina;B. Merriman
通讯作者：
Ronald Fedkiw;A. Marquina;B. Merriman