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Finite Volume Element Methods for Two-Dimensional Three-Temperature Radiation Diffusion Equations

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  20 July 2016

Yanni Gao ,
Xiukun Zhao  and
Yonghai Li
Yanni Gao*
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, Jilin, People's Republic of China
Xiukun Zhao*
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands
Yonghai Li*
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, Jilin, People's Republic of China
*
*Corresponding author. Email addresses:yonghai@jlu.edu.cn (Y.-H. Li), gaoyn10@163.com (Y.-N. Gao), ying509501@126.com (X.-K. Zhao)
*Corresponding author. Email addresses:yonghai@jlu.edu.cn (Y.-H. Li), gaoyn10@163.com (Y.-N. Gao), ying509501@126.com (X.-K. Zhao)
*Corresponding author. Email addresses:yonghai@jlu.edu.cn (Y.-H. Li), gaoyn10@163.com (Y.-N. Gao), ying509501@126.com (X.-K. Zhao)
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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.

Keywords

Two-dimensional three-temperature radiation diffusion equationsFinite volume element methodEnergy conservation propertyRepair techniqueMesh adaptationCutoff method

MSC classification

Secondary: 65N08: Finite volume methods 65N12: Stability and convergence of numerical methods 65N15: Error bounds
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 3 , August 2016 , pp. 470 - 496
Copyright
Copyright © Global-Science Press 2016 

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