More efficient time integration for Fourier pseudospectral DNS of incompressible turbulence

Ketcheson, David I.; Mortensen, Mikael; Parsani, Matteo; Schilling, Nathanael

doi:10.1002/fld.4773

Cited by 8 publications

(4 citation statements)

References 24 publications

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“…This leads to large multidimensional arrays that are distributed effortlessly through mpi4py-fft. Throughout the spectralDNS (https://github.com/ spectralDNS/spectralDNS) project shenfun is being used extensively for Direct Numerical Simulations (DNS) of turbulent flows (Mortensen & Langtangen, 2016, Mortensen (2016, Ketcheson, Mortensen, Parsani, & Schilling (2019)), using arrays with billions of unknowns.…”

Section: Discussionmentioning

confidence: 99%

mpi4py-fft: Parallel Fast Fourier Transforms with MPI for Python

Mortensen¹,

Dalcín²,

Keyes³

2019

JOSS

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Section: Discussionmentioning

confidence: 99%

mpi4py-fft: Parallel Fast Fourier Transforms with MPI for Python

Mortensen¹,

Dalcín²,

Keyes³

2019

JOSS

Self Cite

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“…The solution of linear systems of equations is a time consuming process in numerical simulation of partial differential equations, and has motivated a number of benchmarks [2,4,6,11]. The solution of many partial differential equations requires a choice of discretization methods, in space and typically also in time, each of which presents numerous choices, each of which may have different relative performance on different computer architectures [1,5,9,10,15,[18][19][20]24]. The Klein Gordon equation is chosen as a mini-application because it is relatively simple, can be used to evaluate different time stepping methods and spatial discretization methods, and is representative of seismic wave solvers, and weather codes, all of which use a large amount of high performance computing time [1,10,21,28].…”

Section: Motivationmentioning

confidence: 99%

Benchmarking Solvers for the One Dimensional Cubic Nonlinear Klein Gordon Equation on a Single Core

Muite

Aseeri

2020

Lecture Notes in Computer Science

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Many parallel computing benchmarks specify a specific algorithm that should be used to solve a specific problem, with much effort focused on machine specific optimization of a reference implementation. Since the solution of linear systems of equations, is often the most time consuming part for many problems in high performance scientific computing, a number of recent benchmarks for high performance computers suggest the use of an iterative method for solving sparse linear systems of equations to rank computer performance. Particular methods used include multigrid and conjugate gradients, though other methods such as the fast Fourier transform are also applicable in some cases. The best choice of method may vary with the problem chosen and the hardware the implemented software solution is executed on. Furthermore in solving a scientific computing problem, the level of accuracy can also be important, with some numerical methods being efficient for low accuracy simulations, but others more efficient for high accuracy simulations. Some of these tradeoffs are examined in the numerical solution of the one dimensional Klein Gordon equation on a single core of an x86-64 CPU and a single core of a NEC SX-ACE vector processor.

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“…This standard phase shift technique 5,6 was adopted later for solving the Navier‐Stokes (NS), two‐dimensional (2D) inviscid Boussinesque equations. A number of DNS studies 7‐9 have incorporated the 3/2 padding dealiasing scheme. In our present study, the 2/3 truncation and 3/2 padding schemes are differentiated by filtering out the Fourier components and introducing new samples in the computational domain, respectively.…”

Section: Introductionmentioning

confidence: 99%

An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

Sinhababu

Ayyalasomayajula

2020

Numerical Methods in Fluids

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Summary In this paper, the Random Phase Shift Method (RPSM) dealiasing scheme has been developed with the classical fourth‐order explicit Runge‐Kutta (RK4) method. This scheme is implemented in different benchmark problems to verify its numerical accuracy and computational efficiency where strong gradients are present in the solution. The propagation of aliasing errors through the substeps of RK4 is derived to show the existence of the residual aliasing error terms which results in mild smoothing effect without dissipating the small‐scale flow structures. Smoothness and numerical stability in the solutions obtained from the RPSM scheme also remain well preserved even at under‐resolved conditions. Numerical results agree well with the analytical and the computed solutions from previous studies. RPSM scheme shows a slight delay in the formation of numerical singularity for the inviscid flows but the filtering‐based schemes suffer from early blow‐up problem. We observe that this scheme displays better resolving ability than higher‐order exponential smoothing spectral filter scheme in capturing the strong fronts accurately even at just resolved spatial grid resolutions. Three‐dimensional truncation‐based dealiasing scheme, spherical truncation (SPT) shows vortices generated due to the parasitic currents in the solution of the inviscid three‐dimensional Taylor Green (TG) vortex flows. RPSM displays only the accurate isocontours of vortical field at nearly same computational expenses as the SPT scheme.

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More efficient time integration for Fourier pseudospectral DNS of incompressible turbulence

Cited by 8 publications

References 24 publications

mpi4py-fft: Parallel Fast Fourier Transforms with MPI for Python

mpi4py-fft: Parallel Fast Fourier Transforms with MPI for Python

Benchmarking Solvers for the One Dimensional Cubic Nonlinear Klein Gordon Equation on a Single Core

An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

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