Lagrangian particle method for compressible fluid dynamics
Abstract
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 / multiphase 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 secondorder particlebased algorithm that reduces to the firstorder upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. 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 hyperbolicelliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.
 Authors:

 Stony Brook Univ., Stony Brook, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Stony Brook Univ., Stony Brook, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (SC21); USDOE
 OSTI Identifier:
 1439449
 Alternate Identifier(s):
 OSTI ID: 1548756
 Report Number(s):
 BNL2057152018JAAM
Journal ID: ISSN 00219991; TRN: US1900613
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 362; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Lagrangian fluid mechanics; Particle method; Generalized finite differences
Citation Formats
Samulyak, Roman, Wang, Xingyu, and Chen, Hsin Chiang. Lagrangian particle method for compressible fluid dynamics. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.02.004.
Samulyak, Roman, Wang, Xingyu, & Chen, Hsin Chiang. Lagrangian particle method for compressible fluid dynamics. United States. doi:10.1016/j.jcp.2018.02.004.
Samulyak, Roman, Wang, Xingyu, and Chen, Hsin Chiang. Fri .
"Lagrangian particle method for compressible fluid dynamics". United States. doi:10.1016/j.jcp.2018.02.004. https://www.osti.gov/servlets/purl/1439449.
@article{osti_1439449,
title = {Lagrangian particle method for compressible fluid dynamics},
author = {Samulyak, Roman and Wang, Xingyu and Chen, Hsin Chiang},
abstractNote = {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 / multiphase 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 secondorder particlebased algorithm that reduces to the firstorder upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. 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 hyperbolicelliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.},
doi = {10.1016/j.jcp.2018.02.004},
journal = {Journal of Computational Physics},
number = C,
volume = 362,
place = {United States},
year = {2018},
month = {2}
}
Web of Science
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