# A 3D finite element ALE method using an approximate Riemann solution

## Abstract

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.

- 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:
- 1304832

- Report Number(s):
- LA-UR-16-20312

Journal ID: ISSN 0271-2091

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- International Journal for Numerical Methods in Fluids

- Additional Journal Information:
- Journal Name: International Journal for Numerical Methods in Fluids; Journal ID: ISSN 0271-2091

- Publisher:
- Wiley

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Chiravalle, V. P., and Morgan, N. R.
```*A 3D finite element ALE method using an approximate Riemann solution*. United States: N. p., 2016.
Web. doi:10.1002/fld.4284.

```
Chiravalle, V. P., & Morgan, N. R.
```*A 3D finite element ALE method using an approximate Riemann solution*. United States. doi:10.1002/fld.4284.

```
Chiravalle, V. P., and Morgan, N. R. Tue .
"A 3D finite element ALE method using an approximate Riemann solution". United States.
doi:10.1002/fld.4284. https://www.osti.gov/servlets/purl/1304832.
```

```
@article{osti_1304832,
```

title = {A 3D finite element ALE method using an approximate Riemann solution},

author = {Chiravalle, V. P. and Morgan, N. R.},

abstractNote = {Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.},

doi = {10.1002/fld.4284},

journal = {International Journal for Numerical Methods in Fluids},

number = ,

volume = ,

place = {United States},

year = {Tue Aug 09 00:00:00 EDT 2016},

month = {Tue Aug 09 00:00:00 EDT 2016}

}

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