A Nonlinear Hybrid Finite Volume Scheme for a Cross-Diffusion System in Thin-Film Solar Cell Fabrication
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In multispecies systems, interactions between different species play a key role in determining both the individual behavior of each species and the overall dynamics of the system. The evolution of species concentrations in such systems is often modeled by cross-diffusion systems, which consist of strongly coupled conservation laws with nonlinear fluxes. These structures pose significant analytical and numerical challenges. In this talk, I will focus on the discretization of the Physical Vapor Deposition (PVD) model, which describes the evolution of a gas mixture during the fabrication of thin-film crystalline solar cells. The aim of our work is twofold: to design a numerical scheme applicable on general meshes, and to preserve, at the discrete level, key properties of the continuous model. To this end, we propose a Hybrid Finite Volume scheme, based on a reformulation of the fluxes in terms of entropy variables. We establish the existence of discrete solutions that remain bounded and satisfy a discrete entropy inequality. The convergence of the scheme will also be shown.
