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Title: 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 / 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.

Authors:
 [1];  [2];  [2]
  1. Stony Brook Univ., Stony Brook, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. 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 (SC-21); USDOE
OSTI Identifier:
1439449
Alternate Identifier(s):
OSTI ID: 1548756
Report Number(s):
BNL-205715-2018-JAAM
Journal ID: ISSN 0021-9991; 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 0021-9991
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 / 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.},
doi = {10.1016/j.jcp.2018.02.004},
journal = {Journal of Computational Physics},
number = C,
volume = 362,
place = {United States},
year = {2018},
month = {2}
}

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Figures / Tables:

Figure 1 Figure 1: Simulation results of Sod’s shock tube problem in 1D at t = 1.

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