Year: 2016
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 3 : pp. 470–496
Abstract
Two-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used to approximately describe the evolution of radiation energy within a multi-material system and explain the exchange of energy among electrons, ions and photons. Their highly nonlinear, strong discontinuous and tightly coupled phenomena always make the numerical solution of such equations extremely challenging. In this paper, we construct two finite volume element schemes both satisfying the discrete conservation property. One of them can well preserve the positivity of analytical solutions, while the other one does not satisfy this property. To fix this defect, two as repair techniques are designed. In addition, as the numerical simulation of 2-D 3-T equations is very time consuming, we also devise a mesh adaptation algorithm to reduce the cost. Numerical results show that these new methods are practical and efficient in solving this kind of problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2016.m1523
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 3 : pp. 470–496
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
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A monotone finite volume element scheme for diffusion equations on arbitrary polygonal grids
Nie, Cunyun
Fang, Jianglin
Shu, Shi
Computers & Mathematics with Applications, Vol. 153 (2024), Iss. P.225
https://doi.org/10.1016/j.camwa.2023.11.030 [Citations: 0]