Adaptive moving mesh algorithm based on local reaction rate

Viktória Koncz; Ferenc Izsák; Zoltán Noszticzius; Kristóf Kály-Kullai

doi:10.1016/j.heliyon.2020.e05842

Adaptive moving mesh algorithm based on local reaction rate

Heliyon. 2021 Jan 19;7(1):e05842. doi: 10.1016/j.heliyon.2020.e05842. eCollection 2021 Jan.

Authors

Viktória Koncz¹, Ferenc Izsák², Zoltán Noszticzius¹, Kristóf Kály-Kullai¹

Affiliations

¹ Department of Physics, Budapest University of Technology and Economics, 1521 Budapest, Hungary.
² Department of Applied Analysis and Computational Mathematics, MTA ELTE NumNet Research Group, Eötvös University, 1518 Budapest, Hungary.

Abstract

An empirical mesh adaption algorithm is introduced for modeling one-dimensional reaction-diffusion systems with large moving gradients. Our new algorithm is based on the revelation, that in reaction-diffusion systems the high moving concentration gradients appear nearby to the region where the rate of reaction is maximal, thus the local reaction rate can be used to control the mesh adaption. We found, that the main advantage of such a method is its simplicity and easy implementation. As an example we study an acid-base diode, where large moving gradients appear. The mathematical model of the diode contains several parabolic PDEs, coupled with one elliptic PDE. An r-refinement technique is used and attached to the commercial finite element solver COMSOL. We investigated the time-dependent salt effects of the diode with our developed algorithm. Our mesh adaption method is advantageous for modeling of any reaction-diffusion systems with localized high concentration gradients.

Keywords: Acid-base diode; Adaptive FEM; COMSOL Multiphysics; Moving mesh; Reaction-diffusion systems.