Rodrigo Zelada

Rodrigo Zelada

Postdoctoral Researcher at French Alternative Energies and Atomic Energy Commission.

Posts by Collection

portfolio

3-D convective heat transfer test

We will consider the next test case to valide our shape optimization codes (in following projects): 3-D convective heat transfer test case from Feppon, F., Allaire, G., Dapogny D. and Jolivet, P. Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing (2020). Journal of Computational Physics, 109574. HAL preprint hal-02518207.

publications

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. (2024). 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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Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface

Published in ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2025

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: D. Capatina, F. Caubet, M. Dambrine, and R. Zelada. Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface. ESAIM Math. Model. Numer. Anal., 59(2):999–1021, 2025.
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Shape optimization with Ventcel transmission conditions: application to the design of a heat exchanger

Published in HAL, 2025

This paper aims to optimize the shape of a fluid-to-fluid heat exchanger in order to maximize heat exchange under constraints of energy dissipation and volume. The novelty consists in taking into account the thin layer separating the two fluids by using Ventcel-type second-order transmission conditions. The physical model is then a weakly coupled problem between the steady-state Navier-Stokes equations for the dynamics of the two fluids dynamics and the convection-diffusion equation for the heat. We provide a shape sensitivity analysis and characterize the shape derivatives involved. Finally, we demonstrate the feasibility and effectiveness of the proposed method through 3D numerical simulations.

Recommended citation: Fabien Caubet, Carlos Conca, Marc Dambrine, Rodrigo Zelada. Shape optimization with Ventcel transmission conditions: application to the design of a heat exchanger. 2025. (hal-05033794)
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How to insulate a pipe?

Published in Journal of Optimization Theory and Applications, 2025

This paper focuses on the problem of finding the optimal distribution of a thermal insulator around a pipe. We consider the framework of one fluid inside a pipe of thin width and surrounded by a thermal insulator. We use an asymptotic model to avoid dealing with the thin layer, leading to non-standard transmission conditions which involve discontinuities and second order tangential derivatives. We thus consider the shape optimization problem that aims to minimize the heat flux outside an insulator with a given volume. Then we characterize the shape derivative of the objective functional and perform 3D numerical simulations using the level set evolution method.

Recommended citation: F. Caubet, C. Conca, M. Dambrine, and R. Zelada. How to Insulate a Pipe? J. Optim. Theory Appl., 207(3):46, 2025.
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talks

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

Published:

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.

teaching