Turing patterns in a 3D morpho-chemical bulk-surface reaction-diffusion system for battery modeling

Massimo Frittelli; Ivonne Sgura; Benedetto Bozzini; Massimo Frittelli; Ivonne Sgura; Benedetto Bozzini

doi:10.3934/mine.2024015

Mathematics in Engineering

2024, Volume 6, Issue 2: 363-393. doi: 10.3934/mine.2024015

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Turing patterns in a 3D morpho-chemical bulk-surface reaction-diffusion system for battery modeling

1.
Department of Mathematics and Physics "E. De Giorgi", University of Salento, Lecce 73100, Italy
2.
Department of Energy, Politecnico di Milano, Milano 20156, Italy

Received: 02 July 2023 Revised: 12 February 2024 Accepted: 22 March 2024 Published: 07 April 2024

In this paper we introduce a bulk-surface reaction-diffusion (BS-RD) model in three space dimensions (3D) that extends the so-called DIB morphochemical model to account for the electrolyte contribution in the application, in order to study structure formation during discharge-charge processes in batteries. Here we propose to approximate the model by the bulk-surface virtual element method (BS-VEM) on a tailor-made mesh that proves to be competitive with fast bespoke methods for PDEs on Cartesian grids. We present a selection of numerical simulations that accurately match the classical morphologies found in experiments. Finally, we compare the Turing patterns obtained by the coupled 3D BS-RD model with those obtained with the original 2D version.
- batteries,
- metal electrode,
- electrodeposition,
- bulk-surface reaction-diffusion systems,
- bulk-surface virtual element method,
- Turing patterns
Citation: Massimo Frittelli, Ivonne Sgura, Benedetto Bozzini. Turing patterns in a 3D morpho-chemical bulk-surface reaction-diffusion system for battery modeling[J]. Mathematics in Engineering, 2024, 6(2): 363-393. doi: 10.3934/mine.2024015

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Abstract

In this paper we introduce a bulk-surface reaction-diffusion (BS-RD) model in three space dimensions (3D) that extends the so-called DIB morphochemical model to account for the electrolyte contribution in the application, in order to study structure formation during discharge-charge processes in batteries. Here we propose to approximate the model by the bulk-surface virtual element method (BS-VEM) on a tailor-made mesh that proves to be competitive with fast bespoke methods for PDEs on Cartesian grids. We present a selection of numerical simulations that accurately match the classical morphologies found in experiments. Finally, we compare the Turing patterns obtained by the coupled 3D BS-RD model with those obtained with the original 2D version.

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