Optimal error estimation of themodifiedghost fluid method

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.