# A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

## Abstract

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems 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:
- 1194068

- Report Number(s):
- LA-UR-14-26454

Journal ID: ISSN 0021-9991; PII: S0021999115000947

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 290; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Lagrangian; Eulerian; Arbitrary Lagrangian Eulerian; hydrodynamics; point-centered; Godunov; finite-element; tetrahedron

### Citation Formats

```
Morgan, Nathaniel R., Waltz, Jacob I., Burton, Donald E., Charest, Marc R., Canfield, Thomas R., and Wohlbier, John G.
```*A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes*. United States: N. p., 2015.
Web. doi:10.1016/j.jcp.2015.02.024.

```
Morgan, Nathaniel R., Waltz, Jacob I., Burton, Donald E., Charest, Marc R., Canfield, Thomas R., & Wohlbier, John G.
```*A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes*. United States. doi:10.1016/j.jcp.2015.02.024.

```
Morgan, Nathaniel R., Waltz, Jacob I., Burton, Donald E., Charest, Marc R., Canfield, Thomas R., and Wohlbier, John G. Tue .
"A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes". United States.
doi:10.1016/j.jcp.2015.02.024. https://www.osti.gov/servlets/purl/1194068.
```

```
@article{osti_1194068,
```

title = {A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes},

author = {Morgan, Nathaniel R. and Waltz, Jacob I. and Burton, Donald E. and Charest, Marc R. and Canfield, Thomas R. and Wohlbier, John G.},

abstractNote = {We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.},

doi = {10.1016/j.jcp.2015.02.024},

journal = {Journal of Computational Physics},

number = C,

volume = 290,

place = {United States},

year = {Tue Feb 24 00:00:00 EST 2015},

month = {Tue Feb 24 00:00:00 EST 2015}

}

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