Numerical simulations of underwater explosions using a compressible multi-fluid model

Abstract

We present a novel solver for simulating compressible multi-fluid multiphase flow in underwater explosions (UNDEXs). The developed solver uses a modified version of Saurel's six-equation model, which includes an additional total mixture energy equation to resolve discrepancies in the thermodynamic states predicted under shock conditions. Additionally, we integrate a more precise stiffened gas equation of state (SG-EOS) that is determined using a novel method to enhance the accuracy of predicting experimental data based on a shock Hugoniot curve. We also propose a solution procedure using the modified Saurel's six-equation model on a three-dimensional (3D) structured Cartesian grid system. This involves discretizing the equation system using a Godunov scheme with a two-fluid Harten-Lax-van Leer-Contact approximate Riemann solver and a MUSCL-Hancock primitive scheme with total-variation-diminishing limiters, achieving a second-order extension. Both the dimensional splitting and fractional-step methods are utilized to model one-dimensional (1D) operators, splitting them into sequential operators. The modified model is validated for 1D and 3D problems, including the water–air shock tube, cavitation, shock–bubble interaction, and UNDEX problems in a free field, near a free surface, and near a rigid dam. Our simulations accurately predict the shockwave propagation, shock and free-surface interactions, cavitation evolution, and water jetting impact characteristics, exhibiting satisfactory agreement with those of previous studies. The proposed solver provides insight into the effects of UNDEXs on rigid structures, with potential applications in engineering and defense. The proposed method for determining the SG-EOS parameters can be applied to other areas of research involving high-pressure multi-phase flows.