Lagrangian particle method for compressible fluid dynamics

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

doi:10.1016/j.jcp.2018.02.004

Title: Lagrangian particle method for compressible fluid dynamics

Journal Article · 09 February 2018 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2018.02.004 · OSTI ID:1439449

Samulyak, Roman ^[1]; Wang, Xingyu ^[2]; Chen, Hsin -Chiang ^[2]

Stony Brook Univ., Stony Brook, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
Stony Brook Univ., Stony Brook, NY (United States)

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); USDOE

Grant/Contract Number:: SC0012704

OSTI ID:: 1439449

Alternate ID(s):: OSTI ID: 1548756

Report Number(s):: BNL-205715-2018-JAAM; TRN: US1900613

Journal Information:: Journal of Computational Physics, Vol. 362, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 13 works

Citation information provided by
Web of Science

References (27)

Volume of fluid (VOF) method for the dynamics of free boundaries Hirt, C. W.; Nichols, B. D. Journal of Computational Physics, Vol. 39, Issue 1 https://doi.org/10.1016/0021-9991(81)90145-5	journal	January 1981
An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds Hirt, C. W.; Amsden, A. A.; Cook, J. L. Journal of Computational Physics, Vol. 135, Issue 2 https://doi.org/10.1006/jcph.1997.5702	journal	August 1997
A TSTT integrated FronTier code and its applications in computational fluid physics Fix, Brian; Glimm, James; Li, Xiaolin Journal of Physics: Conference Series, Vol. 16 https://doi.org/10.1088/1742-6596/16/1/064	journal	January 2005
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
Smoothed particle hydrodynamics Monaghan, J. J. Reports on Progress in Physics, Vol. 68, Issue 8 https://doi.org/10.1088/0034-4885/68/8/R01	journal	July 2005
Moving-least-squares-particle hydrodynamics?I. Consistency and stability Dilts, Gary A. International Journal for Numerical Methods in Engineering, Vol. 44, Issue 8 https://doi.org/10.1002/(SICI)1097-0207(19990320)44:8<1115::AID-NME547>3.0.CO;2-L	journal	March 1999
Reproducing kernel particle methods Liu, Wing Kam; Jun, Sukky; Zhang, Yi Fei International Journal for Numerical Methods in Fluids, Vol. 20, Issue 8-9 https://doi.org/10.1002/fld.1650200824	journal	April 1995
Normalized Smoothing Functions for sph Impact Computations Johnson, G. R.; Beissel, S. R. International Journal for Numerical Methods in Engineering, Vol. 39, Issue 16 https://doi.org/10.1002/(SICI)1097-0207(19960830)39:16<2725::AID-NME973>3.0.CO;2-9	journal	August 1996
An improved SPH method: Towards higher order convergence Oger, G.; Doring, M.; Alessandrini, B. Journal of Computational Physics, Vol. 225, Issue 2 https://doi.org/10.1016/j.jcp.2007.01.039	journal	August 2007
Truncation error in mesh-free particle methods Quinlan, N. J.; Basa, M.; Lastiwka, M. International Journal for Numerical Methods in Engineering, Vol. 66, Issue 13 https://doi.org/10.1002/nme.1617	journal	January 2006
Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives Fatehi, R.; Manzari, M. T. Computers & Mathematics with Applications, Vol. 61, Issue 2 https://doi.org/10.1016/j.camwa.2010.11.028	journal	January 2011
CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme Frontiere, Nicholas; Raskin, Cody D.; Owen, J. Michael Journal of Computational Physics, Vol. 332 https://doi.org/10.1016/j.jcp.2016.12.004	journal	March 2017
A new class of Moving-Least-Squares WENO–SPH schemes Avesani, Diego; Dumbser, Michael; Bellin, Alberto Journal of Computational Physics, Vol. 270 https://doi.org/10.1016/j.jcp.2014.03.041	journal	August 2014
On the Construction and Comparison of Difference Schemes Strang, Gilbert SIAM Journal on Numerical Analysis, Vol. 5, Issue 3 https://doi.org/10.1137/0705041	journal	September 1968
Influence of several factors in the generalized finite difference method Benito, J. J.; Ureña, F.; Gavete, L. Applied Mathematical Modelling, Vol. 25, Issue 12 https://doi.org/10.1016/S0307-904X(01)00029-4	journal	December 2001
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations Liska, Richard; Wendroff, Burton SIAM Journal on Scientific Computing, Vol. 25, Issue 3 https://doi.org/10.1137/S1064827502402120	journal	January 2003
Entropy Splitting and Numerical Dissipation Yee, H. C.; Vinokur, M.; Djomehri, M. J. Journal of Computational Physics, Vol. 162, Issue 1 https://doi.org/10.1006/jcph.2000.6517	journal	July 2000
A Well-Posed Kelvin-Helmholtz Instability test and Comparison McNally, Colin P.; Lyra, Wladimir; Passy, Jean-Claude The Astrophysical Journal Supplement Series, Vol. 201, Issue 2 https://doi.org/10.1088/0067-0049/201/2/18	journal	June 2012
Modelling discontinuities and Kelvin–Helmholtz instabilities in SPH Price, Daniel J. Journal of Computational Physics, Vol. 227, Issue 24 https://doi.org/10.1016/j.jcp.2008.08.011	journal	December 2008
von Neumann stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms Balsara, Dinshaw S. Journal of Computational Physics, Vol. 121, Issue 2 https://doi.org/10.1016/S0021-9991(95)90221-X	journal	October 1995
AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov–Poisson equation Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin Journal of Computational Physics, Vol. 316 https://doi.org/10.1016/j.jcp.2016.04.037	journal	July 2016
Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method van Leer, Bram Journal of Computational Physics, Vol. 32, Issue 1 https://doi.org/10.1016/0021-9991(79)90145-1	journal	July 1979
Simulating Free Surface Flows with SPH Monaghan, J. J. Journal of Computational Physics, Vol. 110, Issue 2 https://doi.org/10.1006/jcph.1994.1034	journal	February 1994
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
Quad trees a data structure for retrieval on composite keys Finkel, R. A.; Bentley, J. L. Acta Informatica, Vol. 4, Issue 1 https://doi.org/10.1007/BF00288933	journal	January 1974
Multidimensional binary search trees used for associative searching Bentley, Jon Louis Communications of the ACM, Vol. 18, Issue 9 https://doi.org/10.1145/361002.361007	journal	September 1975
Decomposable searching problems Bentley, Jon Louis Information Processing Letters, Vol. 8, Issue 5 https://doi.org/10.1016/0020-0190(79)90117-0	journal	June 1979

Cited By (1)

Simulation study of the influence of experimental variations on the structure and quality of plasma liners Shih, Wen; Samulyak, Roman; Hsu, Scott C. Physics of Plasmas, Vol. 26, Issue 3 https://doi.org/10.1063/1.5067395	journal	March 2019