Open AccessThe logarithmic mean method for Nonlinear Conductivities at Cell Faces
Author(s) -
Xinxin Jia,
Xiaoli Sun,
Lei Wang,
Hao Zhang,
Xiangchun Li,
Zongrui Hao,
Liya Duuan
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1827/1/012015
Subject(s) - logarithm , diffusion , harmonic mean , dimension (graph theory) , mathematics , nonlinear system , diffusion equation , mathematical analysis , harmonic , work (physics) , logarithmic scale , physics , statistics , thermodynamics , economy , quantum mechanics , acoustics , pure mathematics , economics , service (business)
In this work, logarithmic mean method, which is based on the assumption that the diffusion coefficients profile is linear between nodes, is developed to calculate diffusion coefficients at cell interfaces. The new method is evaluated by solving one dimension steady diffusion equation and convection diffusion equation with strongly non-linear diffusion coefficients. Results indicate that the logarithmic mean method can achieve high precision as the Kirchhoff integral mean method even if the number of nodes is small, while the harmonic mean method needs more nodes to achieve the same accuracy. Furthermore, the logarithmic mean method only needs the diffusion coefficients of nodes, the disadvantage of Kirchhoff method which needs concrete expression of diffusion coefficients and numerous integral operation thus can be overcome.