A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosions

The ghost fluid method for the poor (GFMP) is an elegant, computationally efficient, and nearly conservative method for the solution of two-phase flow problems. It was developed in one dimension for the stiffened gas equation of state (EOS) and one-step time-discretization algorithms. It naturally extends to three dimensions but its extension to higher-order, multi-step time-discretization schemes is not straightforward. Furthermore, the original GFMP and many other ghost fluid methods fail to handle the large density and pressure jumps that are encountered in underwater implosions. Therefore, the GFMP is generalized in this work to an arbitrary EOS and multi-fluid problems with multiple EOSs. It is also extended to three dimensions and developed for higher-order, multi-step time-discretization algorithms. Furthermore, this method is equipped with an exact two-phase Riemann solver for computing the fluxes across the material interface without crossing it. This aspect of the computation is a departure from the standard approach for computing fluxes in ghost fluid methods. It addresses the stiff nature of the two-phase air/water problem and enables a better handling of the large discontinuity of the density at the air/water interface. As the original GFMP, the proposed method is contact preserving, computationally efficient, and nearly conservative. Its superior performance in the presence of large density and pressure jumps is demonstrated for shock-tube problems. Its practicality and accuracy are also highlighted with the three-dimensional simulation of the implosion of an air-filled and submerged glass sphere.