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Finite difference simulations of the Navier-Stokes equations using parallel distributed computing

J.P. De Angeli, A.M.P. Valli, N.C. Reis, A.F. De Souza
Proceedings. 15th Symposium on Computer Architecture and High Performance Computing  
Abstract This paper discusses the implementation of a numerical algorithm for simulating incompressible fluid flows based on the finite difference method and designed for parallel computing platforms  ...  The use of MPI ensures portability across different computing platforms ranging from massively parallel machines to clusters of workstations.  ...  INTRODUCTION In this paper, we study the parallel implementation of the numerical discretization of the Navier-Stokes equations based on the finite difference method suggested by Griebel, Dornseifer and  ... 
doi:10.1109/cahpc.2003.1250333 dblp:conf/sbac-pad/AngeliVRS03 fatcat:blhspmp7tjeffpzrgpxeldsnuu

Development of parallel implementation for the Navier-Stokes equation in doubly connected areas using the fictitious domain method

Almas Temirbekov, Arshyn Altybay, Laura Temirbekovа, Syrym Kasenov
2022 Eastern-European Journal of Enterprise Technologies  
This paper presents a numerical realization of the Navier-Stokes equations in irregular domains using the fictitious domain method with a continuation along with the lowest coefficient.  ...  The finite difference scheme is stable and has high computational accuracy and it gives the possibility to parallelize.  ...  Acknowledgments This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09058430).  ... 
doi:10.15587/1729-4061.2022.254261 fatcat:shy372vuzjfulfj22tfjeyffjy

Page 457 of Mathematical Reviews Vol. , Issue 87a [page]

1987 Mathematical Reviews  
B. 87a:76011 On some solutions of the Navier-Stokes equations using a parallel processor. Comput. Phys. Comm. 37 (1985), no. 1-3, 303-309.  ...  We discuss and comment on the application of some parallel algorithms to obtain solutions of a model Navier- Stokes problem using the ICL distributed array processor.” Gresho, P. M. (1-LLL); Lee, R.  ... 

Simulation of the dynamic two-dimensional Navier-Stokes equation applying the Galerkin methodology

E.J. Canate-Gonzalez, W. Fong-Silva, C.A. Severiche-Sierra, Y.A. Marrugo-Ligardo, J. Jaimes-Morales
2018 Applied Mathematical Sciences  
To finally obtain the numerical solutions of the Navier-Stokes partial differential equations.  ...  A study was carried out based on the discrete approximations of the model and the numerical integration; presenting the mixed formulation of the Navier-Stokes equations that consists of a linear system  ...  InFigure 6 we show the graph of the Blasius equation with its normalized values on the different simulated profiles with the Navier-Stokes equation with the Galerkin methodology.  ... 
doi:10.12988/ams.2018.8242 fatcat:q3fuodcovzdlpfpeicgzj6kjju

Parallel Adaptive Simulation of Coupled Incompressible Viscous Flow and Advective-Diffusive Transport Using Stabilized FEM Formulation

André L. Rossa, Alvaro L.G.A. Coutinho
2012 CLEI Electronic Journal  
In this work we study coupled incompressible viscous flow and advective-diffusive trans- port of a scalar. Both the Navier-Stokes and transport equations are solved using an Eulerian approach.  ...  The implementation is held using the libMEsh finite element library which provides support for parallel adaptive mesh refinement and coarsening.  ...  For this simulation, we disregard the diffusion term of the transport equation (3) . So, the Peclet number does not need to be defined.  ... 
doi:10.19153/cleiej.15.3.1 fatcat:qeydz2znabcijlcvayo373scmu

Page 7106 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
Horton, TIPSI—a time-parallel SIMPLE-based method for the incompressible Navier-Stokes equations (243-256); May-Fun Liou and Ching-Yuen Loh, Parallel computing using a Lagrangian for- mulation (257-269  ...  Hanel, Solution of the Navier-Stokes equations on a massively parallel transputer system (285-296); M. Peri¢c, M. Schafer and E.  ... 


Andrej Lipej
2021 Mechanical Engineering Scientific Journal  
Using classical numerical methods such as the finite element method (FEM) or the finite volume method (FVM), the results are highly dependent on the size and quality of the computational grids.  ...  All the above properties of multiphase flows and their consequences in performing numerical analyses lead us to very long computational times and consequently the use of very powerful computers.  ...  The basic difference between the system of Navier-Stokes equations and LBM is shown in the following two equations: Navier-Stokes equation: 𝜌(𝜕𝑢/𝜕𝑡 + (𝑢 • 𝛻)𝑢) = −𝛻𝑝 + 𝜇∇ 2 𝑢. (1) Lattice Boltzmann  ... 
doi:10.55302/mesj21391-2641025l fatcat:fpsza2u3gjft7fku55a2j2svcy

Accuracy of Discrete-Velocity BGK Models for the Simulation of the Incompressible Navier-Stokes Equations [article]

Marc B. Reider, James D. Sterling (Center for Nonlinear Studies, Los Alamos National Laboratory)
1993 arXiv   pre-print
We introduce a fourth-order scheme and compare results with those of the commonly used lattice Boltzmann discretization and with finite-difference schemes applied to the incompressible Navier-Stokes equations  ...  A Chapman-Enskog expansion of the PDE system predicts that the macroscopic behavior corresponds to the incompressible Navier-Stokes equations with additional terms of order Mach number squared.  ...  The work was supported by the U.S. Department of Energy at Los Alamos National Laboratory. J.D.S. thanks G. Doolen, J.  ... 
arXiv:comp-gas/9307003v1 fatcat:qjbldykma5avvnqnffgdbxd2mi

Spurious currents in finite element based level set methods for two-phase flow

Sara Zahedi, Martin Kronbichler, Gunilla Kreiss
2011 International Journal for Numerical Methods in Fluids  
Also, the Navier-Stokes group and the Parallel Scientific Computing Colloquium are acknowledged for being a platform for discussion and ideas.  ...  My work was supported by the Graduate School in Mathematics and Computing (FMB).  ...  Navier-Stokes equations The structure of the Navier-Stokes system (4.7) is similar to the one of the Stokes system (4.8).  ... 
doi:10.1002/fld.2643 fatcat:lurcjd5gyzhanfvjb2rx6iacwi

Permeability of textile reinforcements: Simulation, influence of shear and validation

B. Verleye, R. Croce, M. Griebel, M. Klitz, S.V. Lomov, G. Morren, H. Sol, I. Verpoest, D. Roose
2008 Composites Science And Technology  
A fast an accurate simulation tool for the permeability of textiles is presented, based on a finite difference discretisation of the Stokes equations.  ...  A finite difference Navier-Stokes solver, NaSt3DGP, was developed at the Institute for Numerical Simulation at the University of Bonn.  ...  ACKNOWLEDGMENTS The work on permeability modelling has been supported by funding from government of Flanders (GBOU 020209) and European Comission (projects ITOOL, AWTOW).  ... 
doi:10.1016/j.compscitech.2008.06.010 fatcat:vhkvou2dvbeyjh2s2knbqjrqpi

Hybrid spectral-element-low-order methods for incompressible flows

Ron Henderson, George Em. Karniadakis
1991 Journal of Scientific Computing  
An analysis of the patching procedure is presented for elliptic problems, and extensions to incompressible Navier-Stokes equations are implemented using an efficient high-order splitting scheme.  ...  In fluid flow simulations of transitional and turbulent flows the high-order discretization (spectral element) is used in the outer part of the domain where the Reynolds number is effectively very high  ...  NAVIER-STOKES ALGORITHM In this section, we extend the iterative patching procedure to the incompressible Navier-Stokes equations for simulations of flows in arbitrarily complex domains.  ... 
doi:10.1007/bf01062115 fatcat:hdlos7xtmrb6thcqji24b42yey

Page 6436 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
The subdomain solvers are based on Chebyshev spectral/finite difference methods, but finite elements, instead of finite differences, could be used to deal with more complicated geometries.”  ...  of Euler or Navier-Stokes equations on unstructured, possibly dynamic, meshes.  ... 

Page 2130 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Here, a method based on solving the Navier-Stokes equations by a finite difference/front tracking technique that allows the inclusion of fully deformable interfaces and surface tension, in addition to  ...  Summary: “A low Mach number approximation (LMNA) of the Navier-Stokes equations is widely used in numerical methods for the simulation of low-speed thermal and athermal flows.  ... 

On Parallel Numerical Algorithms for Simulating Industrial Filtration Problems

R. Čiegis, O. Iliev, Z. Lakdawala
2007 Computational Methods in Applied Mathematics  
The NavierStokes — Brinkmann system of equations is used to describe the laminar flow of incompressible isothermal oil.  ...  Chorin scheme) of the Navier- Stokes equations, where the Brinkmann term is considered in both the prediction and the correction substeps.  ...  Introduction The numerical solution of nonlinear PDEs, such as porous media models or Navier-Stokes equations, require much computational effort.  ... 
doi:10.2478/cmam-2007-0007 fatcat:v7dfp6bn6bffbcftmtzjfh4odq

Parallel-in-Space-and-Time Simulation of the Three-Dimensional, Unsteady Navier-Stokes Equations for Incompressible Flow [chapter]

Roberto Croce, Daniel Ruprecht, Rolf Krause
2014 Modeling, Simulation and Optimization of Complex Processes - HPSC 2012  
Navier-Stokes equations.  ...  Distributed memory parallelization is used in both space and time, featuring up to 2,048 cores in total.  ...  Computational resources were provided by the Swiss National Supercomputing Centre CSCS.  ... 
doi:10.1007/978-3-319-09063-4_2 dblp:conf/hpsc/CroceRK12 fatcat:bpc4mzlhijdepgamq7y5svcrc4
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