Second order upwind Lagrangian particle method for Euler equations

doi:10.1016/j.procs.2016.05.543

Title: Second order upwind Lagrangian particle method for Euler equations

Article Details
Other Related Research

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. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.

Authors:

Samulyak, Roman ^[1] ; Chen, Hsin -Chiang ^[2] ; Yu, Kwangmin ^[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)

Publication Date:: 2016-06-01

Report Number(s):: BNL-112408-2016-JA
Journal ID: ISSN 1877-0509

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), 6-8 Jun 2016; Journal ID: ISSN 1877-0509

Publisher:: Elsevier

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

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

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.

Copy to clipboard


                    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.

Copy to clipboard


                    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.

Copy to clipboard


                    
@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 second-order particle-based 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}

}

Copy to clipboard

Free Publicly Accessible Full Text
Accepted Manuscript (DOE)
Publisher's Version of Record
10.1016/j.procs.2016.05.543
https://doi.org/10.1016/j.procs.2016.05.543

Similar Records

Similar records in DOE PAGES and OSTI.GOV collections:

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

Journal Article Angel, Jordan B. ; Banks, Jeffrey W. ; Henshaw, William D. September 2017 - Journal of Computational Physics

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore »« less
Cited by 1Full Text Available
Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

Journal Article - in OSTI.gov collection Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn ; Shu, Chi-Wang, E-mail: shu@dam.brown.edu September 2014 - Journal of Computational Physics

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore »« less
Full Text Available
Direct discontinuous Galerkin method and its variations for second order elliptic equations

Journal Article Huang, Hongying ; Chen, Zheng ; Li, Jin ; ... August 2016 - Journal of Scientific Computing

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L ² norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore »« less
Cited by 1Full Text Available
A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

Journal Article Mu, Lin ; Wang, Junping ; Ye, Xiu August 2017 - SIAM Journal on Scientific Computing

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore »« less
Full Text Available
Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations

Journal Article - in OSTI.gov collection Wang Haifeng ; Popov, Pavel P. ; Pope, Stephen B. March 2010 - Journal of Computational Physics

We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishingmore »« less
Full Text Available

Access journal articles and accepted manuscripts resulting from DOE research funding

Title: Second order upwind Lagrangian particle method for Euler equations

Access journal articles and accepted manuscripts
resulting from DOE research funding