The accuracy of the modified ghost fluid method for gas-gas Riemann problem

Previous numerical tests have shown that the modified ghost fluid method (MGFM) [T.G. Liu, B.C. Khoo, K.S. Yeo, Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys. 190 (2003) 651-681; T.G. Liu, B.C. Khoo, C.W. Wang, The ghost fluid method for compressible gas-water simulation, J. Comput. Phys. 204 (2005) 193-221) is robust and performs much better than the original GFM [R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys. 152 (1999) 457-492]. In this work, a rigorous analysis is carriedout on the accuracy of the MGFM when applied to the gas-gas Riemann problem. It is shown that at the material interface the MGFM solution approximates the exact solution to at least second-order accuracy in the sense of comparing to the exact solution of a Riemann problem. On the other hand, the results by the original GFM have generally no-order accuracy if the interface is not in normal motion. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.