The ghost fluid method for compressible gas–water simulation T.G. Liu a , B.C. Khoo b,c, * , C.W. Wang a a Institute of High Performance Computing, #01-01 The Capricorn, Singapore Science Park II, Singapore 117528, Singapore b Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore c Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore Received 21 January 2004; received in revised form 5 August 2004; accepted 5 October 2004 Abstract An analysis is carried out for the ghost fluid method (GFM) based algorithm as applied to the gas–water Riemann problems, which can be construed as two single-medium GFM Riemann problems. It is found that the inability to provide correct and consistent Riemann waves in the respective real fluids by these two GFM Riemann problems may lead to inaccurate numerical results. Based on this finding, two conditions are suggested and imposed for the ghost fluid status in order to ensure that correct and consistent Riemann waves are provided in the respective real fluids during the numerical decomposition of the singularity. Using these two conditions to analyse some of the existing GFM-based algorithms such as the original GFM [J. Comput. Phys. 152 (1999) 457], the new version GFM [J. Comput. Phys. 166 (2001) 1; J. Comput. Phys. 175 (2002) 200] and the modified GFM (MGFM) [J. Comput. Phys. 190 (2003) 651], it is found that there are ranges of conditions for each type of solution where either the orig- inal GFM or the new version GFM or both are unable to provide correct or consistent Riemann waves in one of the real fluids. Within these ranges, examples can be found such that either the original GFM or the new version GFM or both are unable to provide accurate results. The MGFM is also found to encounter difficulties when applied to nearly cavitating flow. Various examples are presented to demonstrate the conclusions obtained. The MGFM with proposed modification when applied to nearly cavitating flow is then found to be quite robust and can provide relatively reasonable results. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Gas–water Riemann problem; Ghost fluid method; Approximate Riemann problem solver; Level-set method; GFM Riemann problem 0021-9991/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2004.10.012 * Corresponding author. Tel.: +65 874 2889; fax: +65 779 1459. E-mail addresses: liutg@ihpc.a-star.edu.sg (T.G. Liu), mpekbc@nus.edu.sg (B.C. Khoo). Journal of Computational Physics 204 (2005) 193–221 www.elsevier.com/locate/jcp