Optimal Error Estimation of the Modified Ghost Fluid Method (Communications in Computational Physics, 2010)
The modified ghost fluid method (MGFM) has been shown to be robust andefficient when being applied to multi-medium compressible flows. In this paper, werigorously analyze the optimal error estimation of the MGFM when it is applied tothe multi-fluid Riemann problem. By analyzing the properties of the MGFM and theapproximate Riemann problem solver (ARPS), we show that the interfacial status providedby the MGFM can achieve “third-order accuracy” in the sense of comparing tothe 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 theMGFM is suitable for almost any conditions for predicting the interfacial status, andthat the “natural” approach of “third-order accuracy” is practically less useful. Variousexamples are presented to validate the conclusions made.