Optimal Error Estimation of the Modified Ghost 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.