Développement d'un algorithme numérique monolithique de pseudo-concentration avec une méthode d'éléments finis adaptative pour les écoulements diphasiques en 2D

This work presents the development and implementation of a numerical interface capture method for solving two-phase flows. It includes a brief verification of the model as well as a benchmark case study to test the capabilities of the model. The main objective for this numerical algorithm is to simulate phase splitting and coalescence using simple modeling to capture the physical phenomena present in phase-separated flows. The algorithm is based on the solution of a transport equation associated with a marker field coupled to the Navier-Stokes equations solved according to an Eulerian description using the finite element method. The assembly and the resolution of the system of equations are done using a monolithic approach allowing a better resolution for this type of problems characterized by large ratios of physical properties between phases. The developed method is equipped with a mesh adaptation module which allows it to increase the efficiency of the computation. It is tested with benchmark test cases of increasing difficulty such as the Rayleigh-Taylor instability and the evolution of a breaking wave impacting a wall. It will be seen that some developments are still necessary, but the results presented show the potential and the capacity of this method to reproduce real phenomena and make this model an excellent candidate for the simulation of two-phase flows.