# Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations

## Abstract

In the simulation of laser-driven implosion of a fuel capsule in inertial confinement fusion experiments, a system of two-dimensional 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 two-grid 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). E-mail: 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: S0021-9991(07)00015-0; 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; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Jiang, Jun, Huang, Yunqing, Shu, Shi, and Zeng, Shi.
```*Some new discretization and adaptation and multigrid methods for 2-D 3-T 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 2-D 3-T 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 2-D 3-T 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 2-D 3-T diffusion equations},

author = {Jiang, Jun and Huang, Yunqing and Shu, Shi and Zeng, Shi},

abstractNote = {In the simulation of laser-driven implosion of a fuel capsule in inertial confinement fusion experiments, a system of two-dimensional 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 two-grid 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}

}