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A Lions Domain Decomposition Algorithm for Radiation DiffusionEquations on Non-matching Grids

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  10 November 2015

Li Yin ,
Jiming Wu  and
Zihuan Dai
Li Yin*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
Jiming Wu
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
Zihuan Dai
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China
*
*Corresponding author. Emailaddress: [email protected] (L. Yin), [email protected](J. Wu), [email protected] (Z. Dai)
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Abstract

We develop a Lions domain decomposition algorithm based on a cell functionalminimization scheme on non-matching multi-block grids for nonlinear radiationdiffusion equations, which are described by the coupled radiation diffusionequations of electron, ion and photon temperatures. TheL2 orthogonal projection is applied in the Robintransmission condition of non-matching surfaces. Numerical results show that thealgorithm keeps the optimal accuracy on the whole computational domain, isrobust enough on distorted meshes and curved surfaces, and the convergence ratedoes not depend on Robin coefficients. It is a practical and attractivealgorithm in applying to the two-dimensional three-temperature energy equationsof Z-pinch implosion simulation.

Keywords

Lions domain decompositionradiation diffusion equationsnon-matching gridsSchwarz algorithm

MSC classification

Secondary: 65M06: Finite difference methods 65M55: Multigrid methods; domain decomposition
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 4 , November 2015 , pp. 530 - 548
Copyright
Copyright © Global-Science Press 2015 

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