# Modeling Classical Heat Conduction in FLAG

## Abstract

The Los Alamos National Laboratory FLAG code contains both electron and ion heat conduction modules; these have been constructed to be directly relevant to user application problems. However, formal code verification of these modules requires quantitative comparison to exact solutions of the underlying mathematical models. A wide variety of exact solutions to the classical heat conduction equation are available for this purpose. This report summarizes efforts involving the representation of the classical heat conduction equation as following from the large electron-ion coupling limit of the electron and ion 3T temperature equations, subject to electron and ion conduction processes. In FLAG, this limiting behavior is quantitatively verified using a simple exact solution of the classical heat conduction equation. For this test problem, both heat conduction modules produce nearly identical spatial electron and ion temperature profiles that converge at slightly less than 2nd order to the corresponding exact solution.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1167236

- Report Number(s):
- LA-UR-15-20196

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Ramsey, Scott D., and Hendon, Raymond Cori.
```*Modeling Classical Heat Conduction in FLAG*. United States: N. p., 2015.
Web. doi:10.2172/1167236.

```
Ramsey, Scott D., & Hendon, Raymond Cori.
```*Modeling Classical Heat Conduction in FLAG*. United States. doi:10.2172/1167236.

```
Ramsey, Scott D., and Hendon, Raymond Cori. Mon .
"Modeling Classical Heat Conduction in FLAG". United States.
doi:10.2172/1167236. https://www.osti.gov/servlets/purl/1167236.
```

```
@article{osti_1167236,
```

title = {Modeling Classical Heat Conduction in FLAG},

author = {Ramsey, Scott D. and Hendon, Raymond Cori},

abstractNote = {The Los Alamos National Laboratory FLAG code contains both electron and ion heat conduction modules; these have been constructed to be directly relevant to user application problems. However, formal code verification of these modules requires quantitative comparison to exact solutions of the underlying mathematical models. A wide variety of exact solutions to the classical heat conduction equation are available for this purpose. This report summarizes efforts involving the representation of the classical heat conduction equation as following from the large electron-ion coupling limit of the electron and ion 3T temperature equations, subject to electron and ion conduction processes. In FLAG, this limiting behavior is quantitatively verified using a simple exact solution of the classical heat conduction equation. For this test problem, both heat conduction modules produce nearly identical spatial electron and ion temperature profiles that converge at slightly less than 2nd order to the corresponding exact solution.},

doi = {10.2172/1167236},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Jan 12 00:00:00 EST 2015},

month = {Mon Jan 12 00:00:00 EST 2015}

}