In this paper we address the problem of solving accurately gas–liquid compressible flows without pressure oscillations at the gas–liquid interface. We introduce a new Lagrange-projection scheme based on a random sampling technique introduced by Chalons and Goatin (2007) [7]. We compare it to a ghost fluid approach introduced in Wang et al. (2006), Müller et al. (2009) [25], [20] which is based on the ghost fluid method for the poor (Abgrall and Karni, 2001) [2]. Despite the non-conservative feature of the schemes, we observe the numerical convergence towards the relevant weak solution for shock-contact interaction test cases.
In this paper, we propose a numerical method to model the dynamical behavior of a spherical bubble of vapor and air inside water. The air is assumed to be miscible with the vapor. Each phase is described by a stiffened gas law and the mixture pressure law is recovered by an entropy maximization process. We use an adaptive finite volume solver in order to solve the Euler equations. Numerical experiments are presented that validate our approach.
The numerical simulation of compressible two-phase fluid flows exhibits severe difficulties, in particular, when strong strong variations in the material parameters and high interface velocities are present at the phase boundary. Although several models and discretizations have been developed in the past, a thorough quantitative validation by experimental data and a detailed comparison of numerical schemes are hardly available.Here, two different discretizations are investigated, namely, a non-conservative approach proposed by Saurel and Abgrall [SIAM J Sci Comput 1999;21:1115] and the real ghost fluid method developed by Tang et al. [SIAM J Sci Comput 2006;28:278]. The validation is performed for the case of laser-induced cavitation bubbles collapsing in an infinite medium. For the computations, initial data are deduced implicitly from the experimental data. In particular, the influence of numerical phase transition caused by smearing of the phase boundary is investigated.
