Simulation of drift-diffusion process at high Péclet numbers by the random walk on spheres method

Sabelfeld Karl K. () and Aksyuk Ivan ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia
Aksyuk Ivan: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2022, vol. 28, issue 4, 349-367

Abstract: In this paper, we address the problem of flow simulation at high Péclet numbers by the random walk on spheres (RWS) method. Conventional deterministic methods here face difficulties related to high solution gradients near the boundary in the region known as the boundary layer. In the finite-difference methods, this leads to introduction of very fine meshes which in turn causes problems of stability and high dimensions. The RWS algorithm is mesh free, but the high Péclet number flows should probably also affect the efficiency of simulations. However, it turns out that the RWS algorithm can be well adapted to this case. We present an analysis of the RWS algorithm for different examples of flows with high Péclet number. Simulations are carried out for different boundary conditions and for two-layered material with different diffusion coefficients of exciton’s mobility.

Keywords: Péclet number; boundary layer; RWS algorithm; drift-diffusion equation; exciton; diffusion length; continuity interface condition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/mcma-2022-2128

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