Commun. Comput. Phys., 8 (2010), pp. 403-426.

Optimal Error Estimation of the Modified Ghost Fluid Method

Liang Xu 1, Tiegang Liu 1*

1 LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China.

Received 11 May 2009; Accepted (in revised version) 27 October 2009
Available online 12 March 2010


The modified ghost fluid method (MGFM) has been shown to be robust and efficient when being applied to multi-medium compressible flows. In this paper, we rigorously analyze the optimal error estimation of the MGFM when it is applied to the multi-fluid Riemann problem. By analyzing the properties of the MGFM and the approximate Riemann problem solver (ARPS), we show that the interfacial status provided by the MGFM can achieve "third-order accuracy'' in the sense of comparing to the exact solution of the Riemann problem, regardless of the solution type. In addition, our analysis further reveals that the ARPS based on a doubled shock structure in the MGFM is suitable for almost any conditions for predicting the interfacial status, and that the "natural'' approach of "third-order accuracy'' is practically less useful. Various examples are presented to validate the conclusions made.

AMS subject classifications: 35L45, 65C20, 76T10

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Key words: Modified ghost fluid method, Riemann problem, approximate Riemann problem solver.

*Corresponding author.
Email: (L. Xu), (T. Liu)

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