Positive and free energy satisfying schemes for diffusion with interaction potentials

JOURNAL OF COMPUTATIONAL PHYSICS

卷:419

Article

Liu, Hailiang¹  Maimaitiyiming, Wumaier¹ 

[1] Iowa State Univ, Math Dept, Ames, IA 50011 USA

关键词: Drift-diffusion equations;    Implicit-explicit scheme;    Energy dissipation;    Positivity preserving;   

DOI  :  10.1016/j.jcp.2020.109483

来源: Elsevier

【 摘 要 】

In this paper, we design and analyze second order positive and free energy satisfying schemes for solving diffusion equations with interaction potentials. The semi-discrete scheme is shown to conserve mass, preserve solution positivity, and satisfy a discrete free energy dissipation law for nonuniform meshes. These properties for the fully-discrete scheme (first order in time) remain preserved without a strict restriction on time steps. For the fully second order (in both time and space) scheme, a local scaling limiter is introduced to restore solution positivity when necessary. It is proved that such limiter does not destroy the second order accuracy. In addition, these schemes are easy to implement, and efficient in simulations. Both one and two dimensional numerical examples are presented to demonstrate the performance of these schemes. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free