A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach
arXiv:2003.10413
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.
arXiv comment28 pages, 8 figures
References in corpus (10)
- Efficient Computation of Dendritic Microstructures using Adaptive Mesh Refinement
- Finite element systems of differential forms
- Construction of a pathway map on a complicated energy landscape
- Field Theory of Reaction-Diffusion: Mass Action with an Energetic Variational Approach
- Numerical Study of a Particle Method for Gradient Flows
- Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
- On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach
- A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
- First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
- A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case