Publications

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

Published in , 2024

The objective of this work is to study a diffusion equation with non-standard transmission conditions, which include discontinuities and the Ventcel boundary conditions at the interface. To handle jumps and means of the flux and test-functions, we use broken Sobolev spaces. We present a Nitsche finite element approach and compare it with a discontinuous Galerkin method. Consistency, stability and a priori error estimates are proven and numerically verified.

Recommended citation: Daniela Capatina, Fabien Caubet, Marc Dambrine, Rodrigo Zelada. Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface. 2024. (hal-04587596).
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Shape optimization for a heat exchanger with a thin layer

Published in Monografías matemáticas "García de Galdeano", 2024

This paper focuses on a shape optimization method applied to fluid-to-fluid heat exchangers. We consider the framework of two fluids separated by a solid thin layer (the wall of the pipes) and we perform an asymptotic expansion in order to obtain an approximated model without thin layer. Due to this approximation, the multi-physics problem is reduced to a weak-coupled problem, between the steady-state Navier-Stokes equations for the two fluids dynamics and the convection-diffusion equation for the heat. The aim is then to optimize the shape of the heat exchanger in order to maximize the heat exchange and minimize the pressure drop. Thus, we characterize the shape derivative for the objective functional and perform numerical simulations in two dimensions.

Recommended citation: Caubet, F., Conca, C., Dambrine, M., & Zelada, R. (2022). Shape optimization for a heat exchanger with a thin layer. In Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications (Vol. 43, pp. 51-61).
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