A method for generating moving, orthogonal, area preserving polygonal meshes

Chartrand, Chris; Perot, J. Blair

doi:10.1016/j.jcp.2022.110940

A method for generating moving, orthogonal, area preserving polygonal meshes

Journal Article · Thu Jan 13 23:00:00 EST 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.110940· OSTI ID:1841986

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Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Univ. of Massachusetts, Amherst, MA (United States)

A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Because Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, a generalization of Voronoi polygon meshes was formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method's ability to simulate various physical scenarios is shown. Overall, the advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1841986

Alternate ID(s):: OSTI ID: 1841440

Report Number(s):: SAND--2022-0561J; 702583

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 454; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

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
An Analysis of the Fractional Step Method Perot, J. Blair Journal of Computational Physics, Vol. 108, Issue 1 https://doi.org/10.1006/jcph.1993.1162	journal	September 1993
An Analysis of 1-D Smoothed Particle Hydrodynamics Kernels Fulk, David A.; Quinn, Dennis W. Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0128	journal	June 1996
Introduction to “An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds” Margolin, L. G. Journal of Computational Physics, Vol. 135, Issue 2 https://doi.org/10.1006/jcph.1997.5727	journal	August 1997
The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline Journal of Computational Physics, Vol. 174, Issue 2 https://doi.org/10.1006/jcph.2001.6932	journal	December 2001
Analysis of an Exact Fractional Step Method Chang, Wang; Giraldo, Francis; Perot, Blair Journal of Computational Physics, Vol. 180, Issue 1 https://doi.org/10.1006/jcph.2002.7087	journal	July 2002
Numerical simulation and experiment on dam break problem Hu, Changhong; Sueyoshi, Makoto Journal of Marine Science and Application, Vol. 9, Issue 2 https://doi.org/10.1007/s11804-010-9075-z	journal	May 2010
An introduction to SPH Monaghan, J. J. Computer Physics Communications, Vol. 48, Issue 1 https://doi.org/10.1016/0010-4655(88)90026-4	journal	January 1988
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
A general topology Godunov method Dukowicz, John K.; Cline, Michael C.; Addessio, Frank L. Journal of Computational Physics, Vol. 82, Issue 1 https://doi.org/10.1016/0021-9991(89)90034-X	journal	May 1989
FLIP MHD: A particle-in-cell method for magnetohydrodynamics Brackbill, J. U. Journal of Computational Physics, Vol. 96, Issue 1 https://doi.org/10.1016/0021-9991(91)90270-U	journal	September 1991
Numerical modelling of two-dimensional gas-dynamic flows on a variable-structure mesh Mikhailova, N. V.; Tishkin, V. F.; Tyurina, N. N. USSR Computational Mathematics and Mathematical Physics, Vol. 26, Issue 5 https://doi.org/10.1016/0041-5553(86)90043-1	journal	January 1986
Computational methods in Lagrangian and Eulerian hydrocodes Benson, David J. Computer Methods in Applied Mechanics and Engineering, Vol. 99, Issue 2-3 https://doi.org/10.1016/0045-7825(92)90042-I	journal	September 1992
Delaunay refinement algorithms for triangular mesh generation Shewchuk, Jonathan Richard Computational Geometry, Vol. 22, Issue 1-3 https://doi.org/10.1016/S0925-7721(01)00047-5	journal	May 2002
On the kernel and particle consistency in smoothed particle hydrodynamics Di G. Sigalotti, Leonardo; Klapp, Jaime; Rendón, Otto Applied Numerical Mathematics, Vol. 108 https://doi.org/10.1016/j.apnum.2016.05.007	journal	October 2016
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
Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes Gaburro, Elena; Dumbser, Michael; Castro, Manuel J. Computers & Fluids, Vol. 159 https://doi.org/10.1016/j.compfluid.2017.09.022	journal	December 2017
Study of a complex fluid-structure dam-breaking benchmark problem using a multi-phase SPH method with APR Sun, P. N.; Le Touzé, D.; Zhang, A. -M. Engineering Analysis with Boundary Elements, Vol. 104 https://doi.org/10.1016/j.enganabound.2019.03.033	journal	July 2019
Reconstruction of multi-material interfaces from moment data Dyadechko, Vadim; Shashkov, Mikhail Journal of Computational Physics, Vol. 227, Issue 11 https://doi.org/10.1016/j.jcp.2007.12.029	journal	May 2008
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
Mimetic finite difference method Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.07.031	journal	January 2014
Differential forms for scientists and engineers Blair Perot, J.; Zusi, Christopher J. Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.08.007	journal	January 2014
Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian–Eulerian methods Kucharik, Milan; Shashkov, Mikhail Journal of Computational Physics, Vol. 258 https://doi.org/10.1016/j.jcp.2013.10.050	journal	February 2014
Adaptive reconnection-based arbitrary Lagrangian Eulerian method Bo, Wurigen; Shashkov, Mikhail Journal of Computational Physics, Vol. 299 https://doi.org/10.1016/j.jcp.2015.07.032	journal	October 2015
High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes Gaburro, Elena; Boscheri, Walter; Chiocchetti, Simone Journal of Computational Physics, Vol. 407 https://doi.org/10.1016/j.jcp.2019.109167	journal	April 2020
Pressure evaluation during dam break using weakly compressible SPH Jančík, Petr; Hyhlík, Tomáš EPJ Web of Conferences, Vol. 213 https://doi.org/10.1051/epjconf/201921302030	journal	January 2019
State-of-the-art of classical SPH for free-surface flows Gomez-Gesteira, Moncho; Rogers, Benedict D.; Dalrymple, Robert A. Journal of Hydraulic Research, Vol. 48, Issue sup1 https://doi.org/10.1080/00221686.2010.9641242	journal	January 2010
Use of Barycentric Dual Grids for the Solution of Frequency Domain Problems by FIT Codecasa, L.; Minerva, V.; Politi, M. IEEE Transactions on Magnetics, Vol. 40, Issue 2 https://doi.org/10.1109/TMAG.2004.824547	journal	March 2004
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations Du, Qiang; Emelianenko, Maria; Ju, Lili SIAM Journal on Numerical Analysis, Vol. 44, Issue 1 https://doi.org/10.1137/040617364	journal	January 2006
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
A material point method for snow simulation Stomakhin, Alexey; Schroeder, Craig; Chai, Lawrence ACM Transactions on Graphics, Vol. 32, Issue 4 https://doi.org/10.1145/2461912.2461948	journal	July 2013
The affine particle-in-cell method Jiang, Chenfanfu; Schroeder, Craig; Selle, Andrew ACM Transactions on Graphics, Vol. 34, Issue 4 https://doi.org/10.1145/2766996	journal	July 2015
Smoothed Particle Hydrodynamics Monaghan, J. J. Annual Review of Astronomy and Astrophysics, Vol. 30, Issue 1 https://doi.org/10.1146/annurev.aa.30.090192.002551	journal	September 1992
Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid Koshizuka, S.; Oka, Y. Nuclear Science and Engineering, Vol. 123, Issue 3 https://doi.org/10.13182/NSE96-A24205	journal	July 1996
Geometric Conservation Law and Its Application to Flow Computations on Moving Grids Thomas, P. D.; Lombard, C. K. AIAA Journal, Vol. 17, Issue 10 https://doi.org/10.2514/3.61273	journal	October 1979
Dealing with the Effect of Air in Fluid Structure Interaction by Coupled SPH-FEM Methods Fragassa, Cristiano; Topalovic, Marko; Pavlovic, Ana Materials, Vol. 12, Issue 7 https://doi.org/10.3390/ma12071162	journal	April 2019
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
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
FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS Kühnlein, Christian; Deconinck, Willem; Klein, Rupert Geoscientific Model Development, Vol. 12, Issue 2 https://doi.org/10.5194/gmd-12-651-2019	journal	January 2019

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Mimetic method
Moving mesh
Particle
Voronoi

A method for generating moving, orthogonal, area preserving polygonal meshes

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