# An entropic solver for ideal Lagrangian magnetohydrodynamics

## Abstract

In this paper, the authors adapt to the ideal 1D lagrangian MHD equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system. They use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions. These numerical schemes satisfy an entropy inequality under CFL conditions. In the last section, they describe a particular scheme for the MHD equations and show with some numerical applications its robustness and accuracy. The generalization to full Eulerian multidimensional MHD will be the subject of a forthcoming paper.

- Authors:

- Publication Date:

- Research Org.:
- Dassault System (FR)

- OSTI Identifier:
- 20000628

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 154; Journal Issue: 1; Other Information: PBD: 1 Sep 1999; Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 30 DIRECT ENERGY CONVERSION; 66 PHYSICS; FINITE DIFFERENCE METHOD; MAGNETOHYDRODYNAMICS; LAGRANGIAN FUNCTION; ONE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Bezard, F., and Despres, B.
```*An entropic solver for ideal Lagrangian magnetohydrodynamics*. United States: N. p., 1999.
Web. doi:10.1006/jcph.1999.6300.

```
Bezard, F., & Despres, B.
```*An entropic solver for ideal Lagrangian magnetohydrodynamics*. United States. doi:10.1006/jcph.1999.6300.

```
Bezard, F., and Despres, B. Wed .
"An entropic solver for ideal Lagrangian magnetohydrodynamics". United States. doi:10.1006/jcph.1999.6300.
```

```
@article{osti_20000628,
```

title = {An entropic solver for ideal Lagrangian magnetohydrodynamics},

author = {Bezard, F. and Despres, B.},

abstractNote = {In this paper, the authors adapt to the ideal 1D lagrangian MHD equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system. They use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions. These numerical schemes satisfy an entropy inequality under CFL conditions. In the last section, they describe a particular scheme for the MHD equations and show with some numerical applications its robustness and accuracy. The generalization to full Eulerian multidimensional MHD will be the subject of a forthcoming paper.},

doi = {10.1006/jcph.1999.6300},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = 1,

volume = 154,

place = {United States},

year = {1999},

month = {9}

}

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