A pointcentered 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 pointcentered hydrodynamic (PCH) method. The conservation equations are discretized using an edgebased finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemannlike 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 2stage 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):
 LAUR1426454
Journal ID: ISSN 00219991; PII: S0021999115000947
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 290; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Lagrangian; Eulerian; Arbitrary Lagrangian Eulerian; hydrodynamics; pointcentered; Godunov; finiteelement; tetrahedron
Citation Formats
Morgan, Nathaniel R., Waltz, Jacob I., Burton, Donald E., Charest, Marc R., Canfield, Thomas R., and Wohlbier, John G. A pointcentered 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 pointcentered 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. 2015.
"A pointcentered 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 pointcentered 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 pointcentered hydrodynamic (PCH) method. The conservation equations are discretized using an edgebased finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemannlike 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 2stage 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 = 2015,
month = 2
}
Web of Science

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