Kernels with prescribed surface tension & mobility for threshold dynamics schemes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:337

Article

Esedoglu, Selim¹  Jacobs, Matt¹  Zhang, Pengbo¹ 

[1] Univ Michigan, 530 Church St, Ann Arbor, MI 48105 USA

关键词: Multi-phase flow;    Curvature motion;    Threshold dynamics;   

DOI  :  10.1016/j.jcp.2017.02.023

来源: Elsevier

【 摘 要 】

We show how to construct a convolution kernel that has a desired anisotropic surface tension and desired anisotropic mobility to be used in threshold dynamics schemes for simulating weighted motion by mean curvature of interfaces, including networks of them, in both two and three dimensions. Moreover, we discuss necessary and sufficient conditions for the positivity of the kernel which, in the case of two-phase flow, ensures that the resulting scheme respects a comparison principle and implies convergence to the viscosity solution of the level set formulation of the flow. In particular, we show, in a barrier-type statement, that the kernel cannot possibly be positive unless both the mobility and the surface tension satisfy necessary conditions in three dimensions, and give a complete characterization. Among other results is a threshold dynamics scheme that is guaranteed to dissipate a non-local approximation to the interfacial energy in the fully anisotropic, multiphase setting, using the new kernel construction. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free