Second order upwind lagrangian particle method for euler equations

Roman Samulyak; Hsin Chiang Chen; Kwangmin Yu

doi:10.1016/j.procs.2016.05.543

Second order upwind lagrangian particle method for euler equations

Roman Samulyak
, Hsin Chiang Chen
, Kwangmin Yu

Applied Mathematics and Statistics

Stony Brook University

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

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 second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. Numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.

Original language	English
Pages (from-to)	2433-2437
Number of pages	5
Journal	Procedia Computer Science
Volume	80
DOIs	https://doi.org/10.1016/j.procs.2016.05.543
State	Published - 2016
Event	International Conference on Computational Science, ICCS 2016 - San Diego, United States Duration: Jun 6 2016 → Jun 8 2016

Keywords

Generalized finite differences
Meshless methods
Particle methods
Smooth particle hydrodynamics

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10.1016/j.procs.2016.05.543

Cite this

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title = "Second order upwind lagrangian particle method for euler equations",

abstract = "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 second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. Numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.",

keywords = "Generalized finite differences, Meshless methods, Particle methods, Smooth particle hydrodynamics",

author = "Roman Samulyak and Chen, \{Hsin Chiang\} and Kwangmin Yu",

note = "Publisher Copyright: {\textcopyright} The Authors. Published by Elsevier B.V.; International Conference on Computational Science, ICCS 2016 ; Conference date: 06-06-2016 Through 08-06-2016",

year = "2016",

doi = "10.1016/j.procs.2016.05.543",

language = "English",

volume = "80",

pages = "2433--2437",

journal = "Procedia Computer Science",

issn = "1877-0509",

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TY - JOUR

T1 - Second order upwind lagrangian particle method for euler equations

AU - Samulyak, Roman

AU - Chen, Hsin Chiang

AU - Yu, Kwangmin

N1 - Publisher Copyright: © The Authors. Published by Elsevier B.V.

PY - 2016

Y1 - 2016

N2 - 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 second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. Numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.

AB - 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 second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. Numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.

KW - Generalized finite differences

KW - Meshless methods

KW - Particle methods

KW - Smooth particle hydrodynamics

UR - https://www.scopus.com/pages/publications/84978472620

U2 - 10.1016/j.procs.2016.05.543

DO - 10.1016/j.procs.2016.05.543

M3 - Conference article

AN - SCOPUS:84978472620

SN - 1877-0509

VL - 80

SP - 2433

EP - 2437

JO - Procedia Computer Science

JF - Procedia Computer Science

T2 - International Conference on Computational Science, ICCS 2016

Y2 - 6 June 2016 through 8 June 2016

ER -

Second order upwind lagrangian particle method for euler equations

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Keywords

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