A scalable parallel Poisson solver for three-dimensional problems with one periodic direction

Gorobets, A.; Trias, F. X.; Sòria, M.; Oliva, A.

doi:10.1016/j.compfluid.2009.10.005

Cited by 22 publications

(28 citation statements)

References 27 publications

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“…In Ref. [2], it was shown that, for a simplified case with uniform mesh spacing and second-order spatial discretization, the spectral condition number, j, can be bounded by…”

Section: Poisson Solvermentioning

confidence: 99%

“…The Poisson solver was presented in detail in our previous work [2]. Following the same notation, we firstly define Q R 2 R NxÂNx as an inverse Fourier transform matrix for real-valued problems, i.e.…”

Section: Poisson Solvermentioning

confidence: 99%

“…doi:10.1016/j.compfluid.2011.05.003 a slow convergence, the PCG solver is replaced by a Direct Schurcomplement Decomposition (DSD) method [1]. The overall solver, hereafter named Krylov-Schur-Fourier Decomposition (KSFD) [2], was originally conceived for single-core (also dual-core) processors and therefore, the distributed memory model with message-passing interface (MPI) was used. The range of efficient applicability of this MPI-only implementation is limited up to around 2000-6000 CPU cores depending on the mesh size and the order of the numerical schemes.…”

Section: Introductionmentioning

confidence: 99%

“…the DSD algorithm, and (ii) the parallelization in the periodic direction. For details about the scalability limitations of the KSFD solver, the reader is referred to [2].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid MPI+OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

et al. 2011

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“…In Ref. [2], it was shown that, for a simplified case with uniform mesh spacing and second-order spatial discretization, the spectral condition number, j, can be bounded by…”

Section: Poisson Solvermentioning

confidence: 99%

Section: Poisson Solvermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…the DSD algorithm, and (ii) the parallelization in the periodic direction. For details about the scalability limitations of the KSFD solver, the reader is referred to [2].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid MPI+OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

et al. 2011

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“…Taking a more realistic exponent like p/3 + q % 2 then the method would be 60 2 % 3600 times cheaper than just computing a coarse DNS providing the same levels of accuracy. According to the experience with our code [24] the latter is a more realistic approximation. At this point it must be recalled that the numerical discretization itself is also a regularization (see Section 4.1).…”

Section: How Many Times Cheaper Is the C 4 Regularization?mentioning

confidence: 99%

Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity

et al. 2010

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Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity Trias, F.X.; Verstappen, R.W.C.P.; Gorobets, A.; Soria, M.; Oliva, A. Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Trias, F. X., Verstappen, R. W. C. P., . Parameter-free symmetrypreserving regularization modeling of a turbulent differentially heated cavity. Computers & fluids, 39(10), 1815-1831. DOI: 10.1016/j.compfluid.2010 Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. a b s t r a c tSince direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations [Comput Fluids 2008;37:887] that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore, the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4 Â 10 8 6 Ra 6 10 11 shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with Ra up to 10 17. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of Ra.

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On a Proper Tensor-Diffusivity Model for Large-Eddy Simulation of Buoyancy-Driven Turbulence

Trias

Dabbagh

Gorobets

et al. 2020

Flow Turbulence Combust

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A scalable parallel Poisson solver for three-dimensional problems with one periodic direction

Cited by 22 publications

References 27 publications

Hybrid MPI+OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

Hybrid MPI+OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity

On a Proper Tensor-Diffusivity Model for Large-Eddy Simulation of Buoyancy-Driven Turbulence

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