A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach

2020/03/23 by Chun Liu, Yiwei Wang, Liu, Chun +1 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2003.10413

28 pages, 8 figures

arxiv created 2020/08/21 · arxiv updated 2020/08/24

Abstract

In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our discretization is based on a prescribed energy-dissipation law in terms of the flow map. By employing a discrete energetic variational approach, this scheme preserves the variational structure of the original energy-dissipation law and is energy stable. Plentiful numerical tests show that, by choosing the initial value properly, our methods can produce the desired equilibrium and capture the thin diffuse interface with a small number of mesh points.

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