A pressure-based, compressible, two-phase flow finite volume method for underwater explosions

Abstract

Underwater explosions present many challenges for numerical modeling. The density ratio between explosion gases and the surrounding liquid are typically O(103), and the pressure ratios can be just as high. We develop a cell-centered finite volume method to solve the governing equations of a two-phase homogeneous fluid. Isentropic and isothermal equations of state are used to relate densities and pressure, in lieu of solving an energy equation. A volume fraction is used to distinguish between the disparate phases. A pressure-based, segregated algebraic solution procedure is used to solve for the primitive variables representing volume fraction, velocity, and piezometric pressure. Numerical examples include verification and validation for a number of canonical test cases. In particular, we examine an advecting material interface and show the absence of pressure oscillations across the contact discontinuity. The non-conservative form of our equations does not guarantee exact mass balance, but numerical experiments indicate that this dissipative mechanism has a stabilizing affect on the method. Shock tube and axisymmetric underwater explosion problems are presented to demonstrate the robustness of the algorithm when very large density and pressure discontinuities are present. We simulate a shallow water explosion in three dimensions and examine the effects on the free surface and explosion bubble topology.