# An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR]

## Abstract

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L _{2} norm.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1226207

- Report Number(s):
- LLNL-JRNL-558861

Journal ID: ISSN 1009-0630

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Plasma Science and Technology; Journal Volume: 17; Journal Issue: 2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; hydrodynamic simulation; heat conduction; thermal radiation; adaptive mesh refinement; finite element method

### Citation Formats

```
Fisher, A. C., Bailey, D. S., Kaiser, T. B., Eder, D. C., Gunney, B. T. N., Masters, N. D., Koniges, A. E., and Anderson, R. W..
```*An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR]*. United States: N. p., 2015.
Web. doi:10.1088/1009-0630/17/2/04.

```
Fisher, A. C., Bailey, D. S., Kaiser, T. B., Eder, D. C., Gunney, B. T. N., Masters, N. D., Koniges, A. E., & Anderson, R. W..
```*An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR]*. United States. doi:10.1088/1009-0630/17/2/04.

```
Fisher, A. C., Bailey, D. S., Kaiser, T. B., Eder, D. C., Gunney, B. T. N., Masters, N. D., Koniges, A. E., and Anderson, R. W.. Sun .
"An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR]". United States.
doi:10.1088/1009-0630/17/2/04. https://www.osti.gov/servlets/purl/1226207.
```

```
@article{osti_1226207,
```

title = {An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR]},

author = {Fisher, A. C. and Bailey, D. S. and Kaiser, T. B. and Eder, D. C. and Gunney, B. T. N. and Masters, N. D. and Koniges, A. E. and Anderson, R. W.},

abstractNote = {Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L2 norm.},

doi = {10.1088/1009-0630/17/2/04},

journal = {Plasma Science and Technology},

number = 2,

volume = 17,

place = {United States},

year = {Sun Feb 01 00:00:00 EST 2015},

month = {Sun Feb 01 00:00:00 EST 2015}

}

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