Second Order Threshold Dynamics Schemes for Two Phase Motion by Mean Curvature

11/12/2019
by   Alexander Zaitzeff, et al.
0

The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase setting, a shortcoming it has in common with other related, more recent algorithms such as the equal surface tension version of the Voronoi implicit interface method. As a first, rigorous step in addressing this shortcoming, we present two different second order accurate versions of two-phase threshold dynamics. Unlike in previous efforts in this direction, we present careful consistency calculations for both of our algorithms. The first algorithm is consistent with its limit (motion by mean curvature) up to second order in any space dimension. The second achieves second order accuracy only in dimension two, but comes with a rigorous stability guarantee (unconditional energy stability) in any dimension – a first for high order schemes of its type.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/09/2021

A Monotone, Second Order Accurate Scheme for Curvature Motion

We present a second order accurate in time numerical scheme for curve sh...
research
07/25/2023

A threshold dislocation dynamics method

The Merriman-Bence-Osher threshold dynamics method is an efficient algor...
research
01/13/2020

Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface

We study the dynamics of a droplet placing on an inclined rough surface,...
research
09/28/2022

High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems

This paper develops an implicit family of sub-step integration algorithm...
research
05/12/2022

Assessment of an energy-based surface tension model for simulation of two-phase flows using second-order phase field methods

Second-order phase field models have emerged as an attractive option for...
research
07/23/2019

Γ-convergence for high order phase field fracture: continuum and isogeometric formulations

We consider second order phase field functionals, in the continuum setti...
research
05/20/2021

A cahn-Hilliard multiphase system with mobilities for wetting simulation

This paper tackles the simulation of the wetting phenomenon using a phas...

Please sign up or login with your details

Forgot password? Click here to reset