The numerical simulation of compressible two-phase fluid flows exhibits severe difficulties, in particular, when 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. 21, 1115Comput. 21, (1999) and the real ghost fluid method developed by Tang, Liu and Khoo (SIAM J. Sci. Comput. 28, 278 (2006)). 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.
The concept of fully adaptive multiresolution finite volume schemes has been developed and investigated during the past decade. Here grid adaptation is realized by performing a multiscale decomposition of the discrete data at hand. By means of hard thresholding the resulting multiscale data are compressed. From the remaining data a locally refined grid is constructed.The aim of the present work is to give a self-contained overview on the construction of an appropriate multiresolution analysis using biorthogonal wavelets, its efficient realization by means of hash maps using global cell identifiers and the parallelization of the multiresolution-based grid adaptation via MPI using space-filling curves.Résumé. Le concept des schémas de volumes finis multi-échelles et adaptatifs aété développé et etudié pendant les dix dernières années. Ici le maillage adaptatif est réalisé en effectuant une décomposition multi-échelle des données discrètes proches. En les tronquantà l'aide d'une valeur seuil fixée, les données multi-échelles obtenues sont compressées. A partir de celles-ci, le maillage est raffiné localement.Le but de ce travail est de donner un aperçu concis de la construction d'une analyse appropriée de multiresolution utilisant les fonctions ondelettes biorthogonales, de son efficacité d'application en terme de tables de hachage en utilisant des identification globales de cellule et de la parallélisation du maillage adaptatif multirésolution via MPIà l'aide des courbes remplissantes.
International audienceIn 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 of Chalons and Goatin. We compare it to a Ghost Fluid approach introduced previously. Despite the non-conservative feature of the schemes, we observe the numerical convergence towards the relevant weak solution, for shock-contact interaction test cases. Finally, we apply the new scheme to the computation of the oscillations of a spherical air bubble inside water
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.
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