A Parallel Solver for Incompressible Fluid Flows

Wang, Yushan; Baboulin, Marc; Dongarra, Jack; Falcou, Joel; Fraigneau, Yann; Maître, Olivier Le

doi:10.1016/j.procs.2013.05.207

Cited by 13 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The VSM [14] was chosen as the traditional solution technique because it can be efficiently implemented through the ADI scheme and cyclic reduction [5,6]. It consists of a vorticity transport equation and a Poisson equation for the stream function, which enables the stream function to automatically satisfy the conservation of mass constraints:…”

Section: The Vorticity-stream Function Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Domain decomposition based coupling between the lattice Boltzmann method and traditional CFD methods – Part II: Numerical solution to the backward facing step flow

Velivelli

Bryden

2015

Advances in Engineering Software

View full text Add to dashboard Cite

The lattice Boltzmann method (LBM) and traditional finite difference methods have separate strengths when solving the incompressible Navier-Stokes equations. The LBM is an explicit method with a highly local computational nature that uses floatingpoint operations that involve only local data and thereby enables easy cache optimization and parallelization. However, because the LBM is an explicit method, smaller grid spacing requires smaller numerical time steps during both transient and steady state computations. Traditional implicit finite difference methods can take larger time steps as they are not limited by the CFL condition, but only by the need for time accuracy during transient computations. To take advantage of the strengths of both methods, a multiple solver, multiple grid block approach was implemented and validated for the 2-D Burgers' equation in Part I of this work. Part II implements the multiple solver, multiple grid block approach for the 2-D backward step flow problem. The coupled LBM-VSM solver is found to be faster by a factor of 2.90 (2.87 and 2.93 for Re = 150 and Re = 500, respectively) on a single processor than the VSM for the 2-D backward step flow problem while maintaining similar accuracy. c

show abstract

Section: The Vorticity-stream Function Formulationmentioning

confidence: 99%

“…As noted earlier, the traditional method utilized here is the vorticity-stream function formulation of the Navier-Stokes equations. The vorticity transport equation can be solved efficiently using the ADI method [5], and the stream function equation, which…”

Section: Introductionmentioning

confidence: 99%

Domain decomposition based coupling between the lattice Boltzmann method and traditional CFD methods – Part II: Numerical solution to the backward facing step flow

Velivelli

Bryden

2015

Advances in Engineering Software

View full text Add to dashboard Cite

show abstract

“…Subdivision mesh method of Dynamic quad-tree [9] uses the concept subdivision mesh of quad-tree. In addition ， Perlin noise [10]and Navier-Stokes equation [11] are also effective methods to generate the random height of the water body. But Navier-Stokes equation is very complex and hard to be achieved; bump mapping can achieve fast simulation results ， but it gets rough realistic.…”

Section: Introductionmentioning

confidence: 99%

Water Reflection, Refraction Simulation Based on Perlin Noise and Ray-tracing

Li¹,

Yang²,

Zhao³

2017

IJSIP

View full text Add to dashboard Cite

show abstract

“…Thus the parallelism is achieved with MPI directives at different steps of the algorithm and for solving a linear system at each time step. A lot of papers have been written on this subject: In [3] a good efficiency is achieved up to 60 processors, in [32,31] on big meshes of size 240 3 an efficiency of up to 0.75 for MPI on 48 cores or MPI/OpenMP on 32 cores is obtained. In [28] a preconditioned GMRES method is used to solve Navier-Stokes equations with 3.3 billion unknowns on 65536 cores and a good relative efficiency is reached on fine grids.…”

Section: Introductionmentioning

confidence: 99%

Highly parallel computing of a multigrid solver for 3D Navier–Stokes equations

Bruneau

Khadra

2016

Journal of Computational Science

View full text Add to dashboard Cite

In order to efficiently obtain all frequencies of the solution, a multigrid solver is used to solve the Navier-Stokes equations for incompressible flows. The method uses a cell-by-cell Gauss-Seidel smoother that is not straightforwardly parallelizable. Moreover the coarsest grids are very coarse and cannot be solved in parallel. The proposed method splits the 3D Cartesian computational domain into well balanced sub-domains with respect to two dimensions. Efficient parallel procedures using MPI libraries permit us to get a high strong and weak scalability of the whole parallel software. Comparison is done between MPI and hybrid MPI/OpenMP parallelism.

show abstract

A Parallel Solver for Incompressible Fluid Flows

Cited by 13 publications

References 12 publications

Domain decomposition based coupling between the lattice Boltzmann method and traditional CFD methods – Part II: Numerical solution to the backward facing step flow

Domain decomposition based coupling between the lattice Boltzmann method and traditional CFD methods – Part II: Numerical solution to the backward facing step flow

Water Reflection, Refraction Simulation Based on Perlin Noise and Ray-tracing

Highly parallel computing of a multigrid solver for 3D Navier–Stokes equations

Contact Info

Product

Resources

About