Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results

6 months ago

(original), (preprint), global random walk, Numerical Modeling, paper

Abstract

This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its speed. This situation is usually referred to in the literature as moving-boundary problem with kinetic condition. As a direct application, we propose a numerical scheme to forecast the penetration of small diffusants into a rubber-based material. To check the quality of our results, we compare the numerical results obtained by global random walks either using the analytical solution to selected benchmark cases or relying on finite element approximations with a priori known convergence rates. It turns out that the global random walk concept can be used to produce good quality approximations of the weak solutions to the target class of problems.

Authors

Nicolae Suciu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Surendra Nepal
Department of Mathematics and Computer Science, Karlstad University, Universitetsgatan 2, Karlstad, 65188, Sweden

Yosief Wondmagegne
Department of Mathematics and Computer Science, Karlstad University, Universitetsgatan 2, Karlstad, 65188, Sweden

Magnus Ögren
School of Science and Technology, Örebro University SE-70182, Örebro, Sweden
HMU Research Center, Institute of Emerging Technologies, GR-71004, Heraklion, Greece

Adrian Muntean
Department of Mathematics and Computer Science, Karlstad University, Universitetsgatan 2, Karlstad, 65188, Sweden

Keywords

Global random walk approximation; Stefan-type moving-boundary problems; Finite element approximation, Order of convergence

Paper coordinates

N. Suciu, S. Nepal, Y. Wondmagegne, M. Ögren, A. Muntean, Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results, arXiv:2410.12378, 2024.

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http://arXiv:2410.12378v1 [math.NA] 16 Oct 2024

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