Rodrigo Zelada

Rodrigo Zelada

Applied Mathematics.

Talks and presentations

Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface

May 23, 2023

Talk, MARGAUx PhD Days, Poitiers, France

In this talk, we will study equations with non-standard transmission problems (discontinuous at the interface, Fourier-Robin and/or Ventcell conditions). If the coefficients in the interface boundary conditions are too small (or too high depending on the case), the problem becomes ill-conditioned, hence we propose a Nitsche method to handle it. Then, we consider some models where we want to minimize/maximize some cost functional, with the interface as the unknown. We compute the shape derivatives using the Hadamard method and we use the level-set method to capture the boundary changes. To solve the standard equations we have used FreeFem++ and to solve the non-standard equations we have implemented our own code. Finally, we will give an application to heat exchangers (that are devices that allow the heat exchange between two or more fluids without mixing of fluid), maximizing the heat exchanged and keeping the drop pressure bounded. We consider the framework of two fluids separated by a thin layer (the wall of the pipes) and we perform and asymptotic development in order to obtain a domain that does not depend on the thickness of the layer.