Adaptive reconnection-based arbitrary Lagrangian Eulerian method

Bo, Wurigen; Shashkov, Mikhail

doi:10.1016/j.jcp.2015.07.032

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

Journal Article · Tue Jul 21 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.07.032· OSTI ID:1247151

Bo, Wurigen ^[1]; Shashkov, Mikhail ^[1]

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

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALE method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1247151

Alternate ID(s):: OSTI ID: 1247010

Report Number(s):: LA-UR--15-21737; PII: S0021999115004775

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 299; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (36)

High-order methods and mesh adaptation for Euler equations Alauzet, F. International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8 https://doi.org/10.1002/fld.1739	journal	January 2008
A swept-intersection-based remapping method in a ReALE framework: A SWEPT-INTERSECTION-BASED REMAPPING METHOD Harribey, Thibault; Breil, Jérôme; Maire, Pierre-Henri International Journal for Numerical Methods in Fluids, Vol. 72, Issue 6 https://doi.org/10.1002/fld.3763	journal	December 2012
Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations Du, Qiang; Wang, Desheng International Journal for Numerical Methods in Engineering, Vol. 56, Issue 9 https://doi.org/10.1002/nme.616	journal	January 2003
Conservative Remapping and Region Overlays by Intersecting Arbitrary Polyhedra Grandy, Jeffrey Journal of Computational Physics, Vol. 148, Issue 2 https://doi.org/10.1006/jcph.1998.6125	journal	January 1999
An arbitrary Lagrangian-Eulerian computing method for all flow speeds Hirt, C. W.; Amsden, A. A.; Cook, J. L. Journal of Computational Physics, Vol. 14, Issue 3 https://doi.org/10.1016/0021-9991(74)90051-5	journal	March 1974
Simple adaptive grids for 1 - D initial value problems Dorfi, E. A.; Drury, L. O'C. Journal of Computational Physics, Vol. 69, Issue 1 https://doi.org/10.1016/0021-9991(87)90161-6	journal	March 1987
An adaptive finite element scheme for transient problems in CFD Löhner, Rainald Computer Methods in Applied Mechanics and Engineering, Vol. 61, Issue 3 https://doi.org/10.1016/0045-7825(87)90098-3	journal	April 1987
An efficient linearity-and-bound-preserving remapping method Kucharik, Milan; Shashkov, Mikhail; Wendroff, Burton Journal of Computational Physics, Vol. 188, Issue 2 https://doi.org/10.1016/S0021-9991(03)00187-6	journal	July 2003
Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations Ju, Lili; Du, Qiang; Gunzburger, Max Parallel Computing, Vol. 28, Issue 10 https://doi.org/10.1016/S0167-8191(02)00151-5	journal	October 2002
Optimum quantization and its applications Gruber, Peter M. Advances in Mathematics, Vol. 186, Issue 2 https://doi.org/10.1016/j.aim.2003.07.017	journal	August 2004
Improved initialisation for centroidal Voronoi tessellation and optimal Delaunay triangulation Quinn, Jonathan; Sun, Feng; Langbein, Frank C. Computer-Aided Design, Vol. 44, Issue 11 https://doi.org/10.1016/j.cad.2012.05.002	journal	November 2012
Recent progress in robust and quality Delaunay mesh generation Du, Qiang; Wang, Desheng Journal of Computational and Applied Mathematics, Vol. 195, Issue 1-2 https://doi.org/10.1016/j.cam.2005.07.014	journal	October 2006
Adaptive anisotropic meshing for steady convection-dominated problems Nguyen, Hoa; Gunzburger, Max; Ju, Lili Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 37-40 https://doi.org/10.1016/j.cma.2009.05.001	journal	August 2009
Constrained CVT meshes and a comparison of triangular mesh generators Nguyen, Hoa; Burkardt, John; Gunzburger, Max Computational Geometry, Vol. 42, Issue 1 https://doi.org/10.1016/j.comgeo.2008.04.002	journal	January 2009
ReALE: A Reconnection Arbitrary-Lagrangian–Eulerian method in cylindrical geometry Loubère, Raphaël; Maire, Pierre-Henri; Shashkov, Mikhail Computers & Fluids, Vol. 46, Issue 1 https://doi.org/10.1016/j.compfluid.2010.08.024	journal	July 2011
A multi-material ReALE method with MOF interface reconstruction Breil, Jérôme; Harribey, Thibault; Maire, Pierre-Henri Computers & Fluids, Vol. 83 https://doi.org/10.1016/j.compfluid.2012.08.015	journal	August 2013
A new parallel algorithm for constructing Voronoi tessellations from distributed input data Starinshak, D. P.; Owen, J. M.; Johnson, J. N. Computer Physics Communications, Vol. 185, Issue 12 https://doi.org/10.1016/j.cpc.2014.08.020	journal	December 2014
A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes Maire, Pierre-Henri Journal of Computational Physics, Vol. 228, Issue 7 https://doi.org/10.1016/j.jcp.2008.12.007	journal	April 2009
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
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
Metric-based mesh adaptation for 2D Lagrangian compressible flows Pino, Stéphane Del Journal of Computational Physics, Vol. 230, Issue 5 https://doi.org/10.1016/j.jcp.2010.11.030	journal	March 2011
Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows Belme, A.; Dervieux, A.; Alauzet, F. Journal of Computational Physics, Vol. 231, Issue 19 https://doi.org/10.1016/j.jcp.2012.05.003	journal	August 2012
Numerical Methods in Fluid Dynamics Sod, Gary A. Cambridge University Press https://doi.org/10.1017/CBO9780511753138	journal	January 2010
Experimental and numerical study of the interaction between a planar shock wave and a square cavity Igra, O.; Falcovitz, J.; Reichenbach, H. Journal of Fluid Mechanics, Vol. 313 https://doi.org/10.1017/S0022112096002145	journal	April 1996
Adaptivity with moving grids Budd, Chris J.; Huang, Weizhang; Russell, Robert D. Acta Numerica, Vol. 18 https://doi.org/10.1017/S0962492906400015	journal	May 2009
Asymptotically optimal block quantization Gersho, A. IEEE Transactions on Information Theory, Vol. 25, Issue 4 https://doi.org/10.1109/TIT.1979.1056067	journal	July 1979
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
Adaptive Finite Element Methods for Elliptic PDEs Based on Conforming Centroidal Voronoi–Delaunay Triangulations Ju, Lili; Gunzburger, Max; Zhao, Weidong SIAM Journal on Scientific Computing, Vol. 28, Issue 6 https://doi.org/10.1137/050643568	journal	January 2006
Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations Dukowicz, John K.; Kodis, John W. SIAM Journal on Scientific and Statistical Computing, Vol. 8, Issue 3 https://doi.org/10.1137/0908037	journal	May 1987
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws Tang, Huazhong; Tang, Tao SIAM Journal on Numerical Analysis, Vol. 41, Issue 2 https://doi.org/10.1137/S003614290138437X	journal	January 2003
Centroidal Voronoi Tessellations: Applications and Algorithms Du, Qiang; Faber, Vance; Gunzburger, Max SIAM Review, Vol. 41, Issue 4 https://doi.org/10.1137/S0036144599352836	journal	January 1999
Voronoi diagrams---a survey of a fundamental geometric data structure Aurenhammer, Franz ACM Computing Surveys, Vol. 23, Issue 3 https://doi.org/10.1145/116873.116880	journal	September 1991
On centroidal voronoi tessellation—energy smoothness and fast computation Liu, Yang; Wang, Wenping; Lévy, Bruno ACM Transactions on Graphics, Vol. 28, Issue 4 https://doi.org/10.1145/1559755.1559758	journal	August 2009
R-Adaptive Reconnection-based Arbitrary Lagrangian Eulerian Method-R-ReALE Shashkov, W. Bo and M. Journal of Mathematical Study, Vol. 48, Issue 2 https://doi.org/10.4208/jms.v48n2.15.03	journal	June 2015
Advances in Studies and Applications of Centroidal Voronoi Tessellations Du, Qiang Numerical Mathematics: Theory, Methods and Applications, Vol. 3, Issue 2 https://doi.org/10.4208/nmtma.2010.32s.1	journal	June 2010
2D Centroidal Voronoi Tessellations with Constraints Tournois, Jane Numerical Mathematics: Theory, Methods and Applications, Vol. 3, Issue 2 https://doi.org/10.4208/nmtma.2010.32s.6	journal	June 2010

Cited By (1)

Improving the staggered grid Lagrangian hydrodynamics for modeling multi-material flows Zhao, Hai-bo; Xiao, Bo; Bai, Jing-song arXiv https://doi.org/10.48550/arxiv.1707.02025	preprint	January 2017

Similar Records

Grid adaptation and remapping for arbitrary lagrangian eulerian (ALE) methods

Conference · Mon Dec 31 23:00:00 EST 2001 · OSTI ID:976079

Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows

Journal Article · Fri Sep 30 20:00:00 EDT 2016 · Journal of Computational Physics · OSTI ID:1566106

Tetrahedral Mesh Adaptation for Lagrangian Shock Hydrodynamics

Journal Article · Thu Jun 28 20:00:00 EDT 2018 · Computers and Mathematics with Applications (Oxford) · OSTI ID:1559503

Related Subjects

97 MATHEMATICS AND COMPUTING
H-Adaptation
R-Adaptation
Reconnection-based Arbitrary Lagrangian Methods (ReALE)

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

Citation Formats

References (36)

Cited By (1)

Similar Records

Related Subjects