Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores

Chatterjee, Avik P.; Verma, Mahendra K.; Kumar, Abhishek; Samtaney, Ravi; Hadri, Bilel; Khurram, Rooh Ul Amin

doi:10.1016/j.jpdc.2017.10.014

Cited by 94 publications

(73 citation statements)

References 35 publications

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“…The grid corresponds to a cubical domain of unit dimension. The simulation was performed using a pseudo-spectral code 55,56 . Freeslip and isothermal boundary conditions were employed at the top and bottom plates, and periodic boundary conditions were employed at the side walls.…”

Section: Methodsmentioning

confidence: 99%

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Similarities between the structure functions of thermal convection and hydrodynamic turbulence

et al. 2019

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In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with She and Leveque's predictions [Phys. Rev. Lett. 72, 336-339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

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Section: Methodsmentioning

confidence: 99%

“…We list the values of the energy flux in Table III. We also compute the Fourier transform of our velocity and temperature field data, and compute the spectral energy flux using the following relation 55,56 :…”

Section: B Probability Distribution Function For Velocity Incrementsmentioning

confidence: 99%

Similarities between the structure functions of thermal convection and hydrodynamic turbulence

et al. 2019

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“…where u is the velocity field, Ω = Ωẑ is the angular velocity of the rotating frame, p is the pressure field which includes contributions from centrifugal acceleration, ν is the kinematic viscosity, −2Ω × u is the Coriolis acceleration, and f is the force field. We have simulated these equations in a cube of size (2π) 3 with periodic boundary condition on all the sides using pseudo-spectral code, Tarang 60,61 . We have used fourth-order Runge-Kutta method for time stepping, and Courant-Friedrich-Lewy (CFL) condition to optimize the time stepping (∆t) and 2/3 rule for dealiasing.…”

Section: The Model Systemmentioning

confidence: 99%

On the energy spectrum of rapidly rotating forced turbulence

2018

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In this paper, we investigate the statistical features of the fully developed, forced, rapidly rotating, turbulent system using numerical simulations, and model the energy spectrum that fits well with the numerical data. Among the wavenumbers (k) larger than the Kolmogorov dissipation wavenumber, the energy is distributed such that the suitably non-dimensionized energy spectrum isĒ(k) ≈ exp(−0.05k), where overbar denotes appropriate non-dimensionalization. For the wavenumbers smaller than that of forcing, the energy in a horizontal plane is much more than that along the vertical rotation-axis. For such wavenumbers, we find that the anisotropic energy spectrum, E(k ⊥ , k ) follows the power law scaling, k −5/2 ⊥ k −1/2 , where '⊥'and ' ' respectively refer to the directions perpendicular and parallel to the rotation axis; this result is in line with the Kuznetsov-Zakharov-Kolmgorov spectrum predicted by the weak inertial-wave turbulence theory for the rotating fluids.

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“…The domain is decomposed in the vertical direction (a so-called 1D or slab decomposition) in such a way that the the vertical planes are evenly distributed to all MPI tasks (the slabs will be further decomposed into smaller domains using OpenMP, as described below). A relatively common alternative to this approach is to use a 2D "pencil" decomposition (Yeung et al, 2005;Chatterjee et al, 2018), whose performance implications were considered in M11. If P is the number of MPI tasks, there are M = N z /P planes of the global domain assigned as work to each task, and from the figure, it is clear that each task "owns" a slab of size N x × N y × M points.…”

Section: Problem Descriptionmentioning

confidence: 99%

GPU Parallelization of a Hybrid Pseudospectral Geophysical Turbulence Framework Using CUDA

Rosenberg

Mininni

Reddy³

et al. 2020

Atmosphere

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An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid scheme are reviewed, and heuristics provided to show a potential benefit of the CUDA implementation. The method draws heavily on the CUDA runtime library to handle memory management, and on the cuFFT library for computing local FFTs. The manner in which the interfaces are constructed to these libraries, and ISO bindings utilized to facilitate platform portability, are discussed. CUDA streams are implemented to overlap data transfer with cuFFT computation. Testing with a baseline solver demonstrates significant aggregate speed-up over the hybrid MPI-OpenMP solver by offloading to GPUs on an NVLink-based test system. While the batch streamed approach provides little benefit with NVLink, we see a performance gain of 30% when tuned for the optimal number of streams on a PCIe-based system. It is found that strong GPU scaling is ideal, or slightly better than ideal, in all cases. In addition to speed-up measurements for the fiducial solver, we also consider several other solvers with different numbers of transform operations and find that aggregate speed-ups are nearly constant for all solvers.

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Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores

Cited by 94 publications

References 35 publications

Similarities between the structure functions of thermal convection and hydrodynamic turbulence

Similarities between the structure functions of thermal convection and hydrodynamic turbulence

On the energy spectrum of rapidly rotating forced turbulence

GPU Parallelization of a Hybrid Pseudospectral Geophysical Turbulence Framework Using CUDA

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