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

Chiravalle, V. P.; Morgan, N. R.

doi:10.1002/fld.4284

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

Journal Article · 09 August 2016 · International Journal for Numerical Methods in Fluids

DOI: https://doi.org/10.1002/fld.4284 · OSTI ID:1304832

Chiravalle, V. P. ^[1]; Morgan, N. R. ^[1]

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

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1304832

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

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

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 15 works

Citation information provided by
Web of Science

References (35)

A second-order cell-centered Lagrangian scheme for two-dimensional compressible flow problems Maire, Pierre-Henri; Breil, Jérôme International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8 https://doi.org/10.1002/fld.1564	journal	January 2008
A compatible finite element multi-material ALE hydrodynamics algorithm Barlow, A. J. International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8 https://doi.org/10.1002/fld.1593	journal	January 2008
Curvilinear finite elements for Lagrangian hydrodynamics Dobrev, V. A.; Ellis, T. E.; Kolev, Tz. V. International Journal for Numerical Methods in Fluids, Vol. 65, Issue 11-12 https://doi.org/10.1002/fld.2366	journal	June 2010
3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity: 3D LAGRANGIAN HYDRO SCHEME WITH RIEMANN SOLVER ARTIFICIAL VISCOSITY Loubère, Raphaël; Maire, Pierre-Henri; Váchal, Pavel International Journal for Numerical Methods in Fluids, Vol. 72, Issue 1 https://doi.org/10.1002/fld.3730	journal	September 2012
A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems Loubère, R.; Ovadia, J.; Abgrall, R. International Journal for Numerical Methods in Fluids, Vol. 44, Issue 6 https://doi.org/10.1002/fld.665	journal	February 2004
A uniform strain hexahedron and quadrilateral with orthogonal hourglass control Flanagan, D. P.; Belytschko, T. International Journal for Numerical Methods in Engineering, Vol. 17, Issue 5 https://doi.org/10.1002/nme.1620170504	journal	May 1981
Reconstructing Volume Tracking Rider, William J.; Kothe, Douglas B. Journal of Computational Physics, Vol. 141, Issue 2 https://doi.org/10.1006/jcph.1998.5906	journal	April 1998
Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagrangian Subzonal Masses and Pressures Caramana, E. J.; Shashkov, M. J. Journal of Computational Physics, Vol. 142, Issue 2 https://doi.org/10.1006/jcph.1998.5952	journal	May 1998
A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry Caramana, E. J.; Rousculp, C. L.; Burton, D. E. Journal of Computational Physics, Vol. 157, Issue 1 https://doi.org/10.1006/jcph.1999.6368	journal	January 2000
Numerical Methods for Gasdynamic Systems on Unstructured Meshes Barth, Timothy J. An Introduction to Recent Developments in Theory and Numerics for Conservation Laws https://doi.org/10.1007/978-3-642-58535-7_5	book	January 1999
Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems Després, Bruno; Mazeran, Constant Archive for Rational Mechanics and Analysis, Vol. 178, Issue 3 https://doi.org/10.1007/s00205-005-0375-4	journal	October 2005
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws Sod, Gary A. Journal of Computational Physics, Vol. 27, Issue 1 https://doi.org/10.1016/0021-9991(78)90023-2	journal	April 1978
Use of artificial viscosity in multidimensional fluid dynamic calculations Wilkins, Mark L. Journal of Computational Physics, Vol. 36, Issue 3 https://doi.org/10.1016/0021-9991(80)90161-8	journal	July 1980
An efficient, accurate, simple ale method for nonlinear finite element programs Benson, David J. Computer Methods in Applied Mechanics and Engineering, Vol. 72, Issue 3 https://doi.org/10.1016/0045-7825(89)90003-0	journal	March 1989
A dissipation model for staggered grid Lagrangian hydrodynamics Morgan, Nathaniel R. Computers & Fluids, Vol. 83 https://doi.org/10.1016/j.compfluid.2012.05.018	journal	August 2013
A cell-centered Lagrangian Godunov-like method for solid dynamics Burton, D. E.; Carney, T. C.; Morgan, N. R. Computers & Fluids, Vol. 83 https://doi.org/10.1016/j.compfluid.2012.09.008	journal	August 2013
Verification of a three-dimensional unstructured finite element method using analytic and manufactured solutions Waltz, J.; Canfield, T. R.; Morgan, N. R. Computers & Fluids, Vol. 81 https://doi.org/10.1016/j.compfluid.2013.03.025	journal	July 2013
A three-dimensional finite element arbitrary Lagrangian–Eulerian method for shock hydrodynamics on unstructured grids Waltz, J.; Morgan, N. R.; Canfield, T. R. Computers & Fluids, Vol. 92 https://doi.org/10.1016/j.compfluid.2013.12.021	journal	March 2014
An arbitrary Lagrangian–Eulerian method with adaptive mesh refinement for the solution of the Euler equations Anderson, R. W.; Elliott, N. S.; Pember, R. B. Journal of Computational Physics, Vol. 199, Issue 2 https://doi.org/10.1016/j.jcp.2004.02.021	journal	September 2004
A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension Carré, G.; Del Pino, S.; Després, B. Journal of Computational Physics, Vol. 228, Issue 14 https://doi.org/10.1016/j.jcp.2009.04.015	journal	August 2009
A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry Maire, Pierre-Henri Journal of Computational Physics, Vol. 228, Issue 18 https://doi.org/10.1016/j.jcp.2009.06.018	journal	October 2009
A comparative study of interface reconstruction methods for multi-material ALE simulations Kucharik, Milan; Garimella, Rao V.; Schofield, Samuel P. Journal of Computational Physics, Vol. 229, Issue 7 https://doi.org/10.1016/j.jcp.2009.07.009	journal	April 2010
ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method Loubère, Raphaël; Maire, Pierre-Henri; Shashkov, Mikhail Journal of Computational Physics, Vol. 229, Issue 12 https://doi.org/10.1016/j.jcp.2010.03.011	journal	June 2010
A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction Galera, Stéphane; Maire, Pierre-Henri; Breil, Jérôme Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.04.019	journal	August 2010
An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics Morgan, Nathaniel R.; Kenamond, Mark A.; Burton, Donald E. Journal of Computational Physics, Vol. 250 https://doi.org/10.1016/j.jcp.2013.05.015	journal	October 2013
A Lagrangian staggered grid Godunov-like approach for hydrodynamics Morgan, Nathaniel R.; Lipnikov, Konstantin N.; Burton, Donald E. Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.12.013	journal	February 2014
A Godunov-like point-centered essentially Lagrangian hydrodynamic approach Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E. Journal of Computational Physics, Vol. 281 https://doi.org/10.1016/j.jcp.2014.10.048	journal	January 2015
Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR) Burton, D. E.; Morgan, N. R.; Carney, T. C. Journal of Computational Physics, Vol. 299 https://doi.org/10.1016/j.jcp.2015.06.041	journal	October 2015
A second-order compatible staggered Lagrangian hydrodynamics scheme using a cell-centered multidimensional approximate Riemann solver Loubère, Raphaël; Maire, Pierre-Henri; Váchal, Pavel Procedia Computer Science, Vol. 1, Issue 1 https://doi.org/10.1016/j.procs.2010.04.216	journal	May 2010
A Method for the Numerical Calculation of Hydrodynamic Shocks VonNeumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, Issue 3 https://doi.org/10.1063/1.1699639	journal	March 1950
A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme SIAM Journal on Scientific Computing, Vol. 29, Issue 4 https://doi.org/10.1137/050633019	journal	January 2007
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N. SIAM Journal on Scientific Computing, Vol. 34, Issue 5 https://doi.org/10.1137/120864672	journal	January 2012
Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing Karman, Steve L.; Anderson, W. Kyle; Sahasrabudhe, Mandar AIAA Journal, Vol. 44, Issue 6 https://doi.org/10.2514/1.15929	journal	June 2006
Staggered Lagrangian Discretization Based on Cell-Centered Riemann Solver and Associated Hydrodynamics Scheme Maire, Pierre-Henri; Loubère, Raphaël; Váchal, Pavel Communications in Computational Physics, Vol. 10, Issue 4 https://doi.org/10.4208/cicp.170310.251110a	journal	October 2011
Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing Karman, Steve; Anderson, W.; Sahasrabudhe, Mandar 43rd AIAA Aerospace Sciences Meeting and Exhibit https://doi.org/10.2514/6.2005-923	conference	June 2005

Similar Records

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

Journal Article · 2015 · Journal of Computational Physics · OSTI ID:1770013

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; +3 more

Second order multidimensional sign-preserving remapping for ALE methods

Conference · 2010 · OSTI ID:1044882

Hill, Ryan N; Szmelter, J

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics]

Journal Article · 2012 · SIAM Journal on Scientific Computing · OSTI ID:1226956

Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.

Related Subjects

97 MATHEMATICS AND COMPUTING

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

Citation Formats

References (35)

Similar Records

Related Subjects