A weakly compressible free-surface flow solver for liquid–gas systems using the volume-of-fluid approach

Numerical modeling of the dynamics of bubble oscillations subjected to fast variations in the ambient pressure with a coupled level set and volume of fluid method

“…(7). However, considering uniform gas pressure inside the bubble is not pertinent to computing the interaction of a bubble with pressure waves (shock waves) when the Mach number is high [37,38]. It is worth noting that the first term cannot be neglected, as in the case of fast variations of the ambient pressure with high frequency and very short time scales resulting in the rapid volume and shape oscillations of gas bubbles in liquid.…”

“…However, the handling of thermodynamic pressure is not straightforward and becomes complex to exactly estimate 043107-2 it near the interface with the two pressure model. Another kind of method based on the two-phase flow formulation of a weakly compressible volume of fluid (VOF) approach with pressure-projection method is developed by Heyns et al [37]. The method contains a single-fluid Eulerian finite volume approach of Navier-Stokes equations in low Mach number conditions.…”

“…However, the surface tension effects are not taken into account in their model. Furthermore, it is noteworthy that the methods developed in [34,37] have not further been extended to the problems of the pressure driven oscillating gas bubble system when it is strongly deformed. Most recently, Huber et al [38] and Duret et al [39] have proposed a compressible two-phase flow solver for the numerical simulation of low Mach number liquid-gas flows with surface tension effects using the LS method and the CLSVOF method, respectively.…”

“…This work, which pursues the idea of the aforementioned numerical works [34,37], presents a numerical method based on a single-fluid approach of weakly compressible axisymmetric Navier-Stokes equations for the numerical simulation of bubble oscillations in response to pressure variations in the ambient liquid. The method uses the interface capturing procedure based on the CLSVOF algorithm [31] to compute the interface motion.…”

A particle method for two-phase flows with compressible air pocket

“…Nevertheless, for problems where compression of air is significant, it would be necessary to account for air compressibility while treating water as incompressible. Therefore, the incompressible 2P-CPM [14] is further improved by accounting for air compressibility in the present study such that water-air flows with air entrapment can be accurately simulated.To model incompressible or weakly compressible flows, the approach of artificial compressibility was used by other researchers [4,15], by replacing the transient density term in the continuity term with a pressure term through an EOS. Nevertheless, employing the real compressibility parameter by 1P-CPM and 2P-CPM are similar for the time period without an entrapped air pocket.…”