Second order upwind Lagrangian particle method for Euler equations
A new second order upwind 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) an upwind secondorder particlebased algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.
 Authors:

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 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:
 Report Number(s):
 BNL1124082016JA
Journal ID: ISSN 18770509
 Grant/Contract Number:
 SC00112704
 Type:
 Accepted Manuscript
 Journal Name:
 Procedia Computer Science
 Additional Journal Information:
 Journal Volume: 80; Journal Issue: C; Conference: International Conference on Computational Science 2016, San Diego, CA (United States), 68 Jun 2016; Journal ID: ISSN 18770509
 Publisher:
 Elsevier
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; particle methods; generalized finite differences; meshless methods; smooth particle hydrodynamics
 OSTI Identifier:
 1324262
Samulyak, Roman, Chen, Hsin Chiang, and Yu, Kwangmin. Second order upwind Lagrangian particle method for Euler equations. United States: N. p.,
Web. doi:10.1016/j.procs.2016.05.543.
Samulyak, Roman, Chen, Hsin Chiang, & Yu, Kwangmin. Second order upwind Lagrangian particle method for Euler equations. United States. doi:10.1016/j.procs.2016.05.543.
Samulyak, Roman, Chen, Hsin Chiang, and Yu, Kwangmin. 2016.
"Second order upwind Lagrangian particle method for Euler equations". United States.
doi:10.1016/j.procs.2016.05.543. https://www.osti.gov/servlets/purl/1324262.
@article{osti_1324262,
title = {Second order upwind Lagrangian particle method for Euler equations},
author = {Samulyak, Roman and Chen, Hsin Chiang and Yu, Kwangmin},
abstractNote = {A new second order upwind 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) an upwind secondorder particlebased algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.},
doi = {10.1016/j.procs.2016.05.543},
journal = {Procedia Computer Science},
number = C,
volume = 80,
place = {United States},
year = {2016},
month = {6}
}