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Robust Computational Algorithm for Parallelized Simulations of Liesegang Patterns
Última modificación: 24-10-2024
Resumen
Liesegang patterns are unevenly spaced colored bands that can be obtained from the reaction of two specific substances, under diffusion-dominated conditions. The reactions involve the precipitation of one compound (most frequently salt crystals) which in turn forms the bands. This phenomenon has been studied more than a century ago but currently is getting increased interest since it can pose as an alternative for the bottom-up manufacturing of functional nano- and microstructures. In a previous work, a comprehensive numerical strategy for the numerical simulations of the dynamics of these processes able to solve the discontinuous nature of the phenomena, was presented. In such work, the well-posedness of the numerical formulation for the Liesegang pattern formation process was demonstrated. Even though precisely validated against literature results, the computational algorithm developed for OpenFOAM proved insufficient to simulate complex domains that demand extra computational cost, since it was not able to run on distributed memory platforms. The main characteristic of the strategy used to simulate the dynamics behind pattern formation is the communication of information in local domains around a specific area, to trigger or inhibit precipitation reactions. In this work, we propose a code framework that allows this original algorithm to be executed in parallel. OpenFOAM provides standardized tools to communicate specific information in certain ways, but as there were special needs for this phenomenon (i.e. share information on whether the reactions should be triggered or inhibited in a location according to the implemented model), the primitives provided by OpenFOAM were used. The developed framework was seamlessly integrated with the previous algorithm to simulate the pattern formation, and was tested against serial runs of the same scenarios, reducing greatly the simulation times but also allowing to obtain more precise results or enabling more complex domains, as far as denser meshes are allowed.
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