Séminaire des Doctorant·e·s :

Le 06 novembre 2024 à 17:00 - Salle 109

Présentée par Spadotto Aurelio Edoardo - Université Montpellier

A Discrete De Rham scheme for an elliptic problem with an interface: application to the Leaky Dielectric Model

The flow of biological membranes such as red blood cells is influenced, among other factors, by the action of external electric fields. Starting with a quick introduction of the flow-structure model describing the motion of the membrane, we will focus on the problem of finding the electric tension at the interface. This question drives the development of a numerical scheme to solve an elliptic problem with jump conditions imposed at an internal interface. The Discrete de Rham scheme is chosen because of its flexibility with respect to interface motion conjugated with the possibility of a priori estimates in the fashion of the Finite Element Method. We will conclude by showing numerical simulations of the membrane charging process in a uniform external field and discuss the coupling of the electric solver with an HHO solver to implement membrane motion