Some new discretization and adaptation and multigrid methods for 2D 3T diffusion equations
Abstract
In the simulation of laserdriven implosion of a fuel capsule in inertial confinement fusion experiments, a system of twodimensional diffusion equations coupled with electron, iron and photon temperature are widely used to approximately describe the process of energy across multiple materials and the exchange of energy among electrons, irons and photons. The numerical solution of such equations is always challenging because of its strong nonlinear phenomena and strong discontinuous interfaces. In this article, we design a symmetric finite volume method, develop the corresponding preconditioning technique, and propose a mesh adaptation algorithm based on Hessian matrix and a twogrid method. Using these new methods, we demonstrate that the energy conservation error and computation efficiency of the integrated algorithm are much better than classical method.
 Authors:
 Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan City, YangGuTang, Xiangtan, Hunan 411105 (China)
 Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan City, YangGuTang, Xiangtan, Hunan 411105 (China). Email: huangyq@xtu.edu.cn
 Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)
 Publication Date:
 OSTI Identifier:
 20991581
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 224; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2007.01.013; PII: S00219991(07)000150; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CALCULATION METHODS; COMPUTERIZED SIMULATION; DIFFUSION EQUATIONS; ELECTRON TEMPERATURE; ELECTRONS; ENERGY CONSERVATION; IMPLOSIONS; INERTIAL CONFINEMENT; IRON; LASERS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PHOTON TEMPERATURE; PHOTONS; TWODIMENSIONAL CALCULATIONS
Citation Formats
Jiang, Jun, Huang, Yunqing, Shu, Shi, and Zeng, Shi. Some new discretization and adaptation and multigrid methods for 2D 3T diffusion equations. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2007.01.013.
Jiang, Jun, Huang, Yunqing, Shu, Shi, & Zeng, Shi. Some new discretization and adaptation and multigrid methods for 2D 3T diffusion equations. United States. doi:10.1016/j.jcp.2007.01.013.
Jiang, Jun, Huang, Yunqing, Shu, Shi, and Zeng, Shi. Sun .
"Some new discretization and adaptation and multigrid methods for 2D 3T diffusion equations". United States.
doi:10.1016/j.jcp.2007.01.013.
@article{osti_20991581,
title = {Some new discretization and adaptation and multigrid methods for 2D 3T diffusion equations},
author = {Jiang, Jun and Huang, Yunqing and Shu, Shi and Zeng, Shi},
abstractNote = {In the simulation of laserdriven implosion of a fuel capsule in inertial confinement fusion experiments, a system of twodimensional diffusion equations coupled with electron, iron and photon temperature are widely used to approximately describe the process of energy across multiple materials and the exchange of energy among electrons, irons and photons. The numerical solution of such equations is always challenging because of its strong nonlinear phenomena and strong discontinuous interfaces. In this article, we design a symmetric finite volume method, develop the corresponding preconditioning technique, and propose a mesh adaptation algorithm based on Hessian matrix and a twogrid method. Using these new methods, we demonstrate that the energy conservation error and computation efficiency of the integrated algorithm are much better than classical method.},
doi = {10.1016/j.jcp.2007.01.013},
journal = {Journal of Computational Physics},
number = 1,
volume = 224,
place = {United States},
year = {Sun May 20 00:00:00 EDT 2007},
month = {Sun May 20 00:00:00 EDT 2007}
}

On choosing a nonlinear initial iterate for solving the 2D 3T heat conduction equations
The 2D 3T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficultmore »