Estimateur d’erreur efficace a posteriori pour la résolution d’écoulements granulaires immergés

Details

Supervisors

Legat, Vincent ; Lambrechts, Jonathan

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées

Abstract

enFor finite element methods, the mesh is a fundamental tool that will influence the whole computation: the computational time, the accuracy of the results and, the stability of the model. Getting an accurate numerical solution in a short period is the main challenge of many finite element codes of this century. One of the way we could tackle the problem is to develop an error estimator to be further used in an adaptive strategy. To respond to this challenge, we implemented an adaptive algorithm based on a gradient recovery estimator over the velocity and pressure field. This estimator is easy to implement in existing codes because it does not require knowledge about the problem. It was applied to immersed granular flows and, we obtained valuable results for the test case of a falling cloud of grains in a highly viscous fluid. The mesh was refined around the falling cloud and, the queue formed behind it was also correctly captured. To further enhance the accuracy of the solution, we developed a local mesh adaptation algorithm. The local adaptation reduces the numerical diffusion introduced by the interpolation of the solution over the new mesh. This adaptive technique is inspired by the work of Bank and Sherman.