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首页> 外文期刊>Journal of Computational Physics >Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem
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Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem

机译：多重黎曼问题的各种幻影流体方法的精度和守恒误差

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摘要

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.
机译：由于（原始）鬼流体方法（OGFM）由Fedkiw等人提出。 1999年[5]，随后又开发了其他一系列基于GFM的方法，例如气水版GFM（GWGFM），改进的GFM（MGFM）和实际GFM（RGFM）。但是，尚未对各种GFM的准确性和保护误差进行系统分析。在本文中，我们开发了一种技术，用于将这些不同的GFM应用于带有一般状态方程（EOS）的多媒体黎曼问题时，会严格分析其精度和守恒误差。通过分析和比较每个GFM提供的界面状态与原始的多个中黎曼问题的精确状态，我们表明，界面处理的精确度在与DMF的精确解进行比较的意义上可以达到“三阶精确度” MGFM和RGFM是原始的多介质Riemann问题，而当接口方法实际上接近平衡时，OGFM和GWGFM最多具有“一阶精度”。结合当地的保护错误也可以得出类似的结论。从数值的角度出发，采用了一种特殊的测试方法来验证这些理论结论。

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