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.

A review of underwater shock and fluid–structure interactions

“…For fluids, most commercial solvers do not handle fluid phase change (such as cavitation effects) well, if at all. This is a huge limitation for near-field explosions, but there is much ongoing work trying to address such limitations with fluid solvers (Tian et al 2021;Yu et al 2022Yu et al , 2023aYu, Song & Choi 2023b). Modelling the dynamic and failure behaviour of complex materials such as composites is also challenging for solids.…”

Mathematical modeling of a novel fractional-order monkeypox model using the Atangana–Baleanu derivative

“…Generally, when we consider fractional calculus, it is just an extended version of ordinary calculus (Agaba et al, 2017;Ahmed et al, 2021;Agusto, 2017;Ayinla et al, 2021;Biswas 2017a;Cai et al, 2017) where the order of the derivatives or integrals can be taken arbitrary as real or complex values (Yu et al, 2023;Huang and Yu, 2023;Parmar et al, 2023;Tasman, 2015;Zuo et al, 2022). The motivation behind replacing ordinary calculus with fractional operators is that the latter can prove to be much more efficient in modeling various real-world problems specifically when the dynamics of the system keep changing with respect to the inherent constraints defined for the given system (Jan et al, 2019;Chinnathambi et al, 2021;Kumar et al, 2019) Also, fractional derivatives can be local and non-local in nature.…”