Numerical modeling of erosion using an improvement of the extended finite element method

Abstract

ABSTRACT. We present in this paper a numerical model of the erosion of a soil that accounts for both the flow in the open fluid and the flow of fluid through the porous soil. The interface between the open fluid and the soil is represented using a level-set function, and the erosion is controlled by the shear stress vector. The evaluation of the approximate value of this gradient is particularly focused on, and an improved method, called XFE+ method, is presented. Numerical results in 2D and 3D illustrate the accuracy and the potentiality of this method.RÉSUMÉ. Cet article décrit un modèle numérique d'érosion du sol, qui prend en compte à la fois le fluide dans le sol, considéré comme un milieu poreux, et le fluide extérieur. L'interface entre les deux milieux est représentée à l'aide d'une fonction level-set, et l'érosion est contrôlée par le gradient de la vitesse du fluide. Nous nous concentrons particulièrement sur l'évaluation numérique de ce gradient, et introduisons une méthode, appelée méthode XFE+, pour l'améliorer. Des résultats numériques en 2D et 3D montrent la précision et les potentialités de cette mé-thode.

A stable extended FEM formulation for multi‐phase problems enforcing the accuracy of the fluxes through Lagrange multipliers

“…The resulting formulation was unfortunately very dependent on the type of elements that were used, and no stability analysis was possible. The general form of the mixed weak formulation presented at Section 5 was then briefly sketched in , but without the stability analysis and examples presented here. The adopted methodology is based in enforcing continuity of the flux across the interface using Lagrange multipliers.…”