期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 386, 期 -, 页码 22-36出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.02.028
关键词
Fokker-Planck equation; Harmonic-mean approximation; Positivity; Mass conservation; Condition number
资金
- Natural Science Foundation of Jiangsu Province [BK20160302]
- National Natural Science Foundation of China [11601361, 21773165]
- Soochow University [Q410700415]
In this work, we design and analyze a conservative, positivity preserving, and free energy dissipating finite difference method for the multi-dimensional nonlocal Fokker-Planck (FP) equation. Based on a non-logarithmic Landau transformation, a central-differencing spatial discretization using harmonic-mean approximations is developed. Both forward and backward Euler discretizations in time are employed to derive an explicit scheme and a linearized semi-implicit scheme, respectively. Three desired properties that are possessed by analytical solutions: i) mass conservation, ii) free-energy dissipation, and iii) positivity, are proved to be maintained at discrete level. Remarkably, numerical analysis demonstrates that the semi-implicit time discretization ensures the property of positivity preserving unconditionally. Due to the advantages brought by the harmonic-mean approximations, an estimate on the upper bound of the condition number of the resulting coefficient matrix is further established for the semi-implicit scheme. Extensive numerical tests are performed to validate aforementioned properties numerically. (C) 2019 Elsevier Inc. All rights reserved.
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