A new parallel strategy for two-dimensional incompressible flow simulations using pseudo-spectral methods

Abstract

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Z. Yin, H.J.H. Clercx, D.C. Montgomery, An easily implemented task-based parallel scheme for the Fourier pseudo-spectral solver applied to 2D Navier-Stokes turbulence, Comput. Fluid 33 (2004) 509] and parallelized Fast Fourier Transform scheme. The performances of the resulting MPI Fortran90 codes with the new procedure on SGI 3800 are reported. For fixed resolution of the same problem, the peak speed of the new scheme can be twice as fast as the old parallel methods. The parallelized codes are used to solve some challenging numerical problems governed by the Navier-Stokes equations and the Boussinesq equations. Two interesting physical problems, namely, the double-valued x-w structure in two-dimensional decaying turbulence and the collapse of the bubble cap in the Boussinesq simulation, are solved by using the proposed parallel algorithms.

Computation-Communication Overlap Techniques for Parallel Spectral Calculations in Gyrokinetic Vlasov Simulations

“…In the GKV code, perpendicular dynamics is solved by using the spectral method [3] with Fast Fourier Transform (FFT) algorithms [4]. The most commonly used parallel multi-dimensional FFT is the transpose-split method [5], and one can find many literatures about the spectral or pseudo-spectral methods with parallel FFTs (e.g., 2D FFTs [6], 3D FFTs with the slab decomposition [7] and with the pencil decomposition [8]). While the transpose communications may degrade scalability, it is reported that the overlap of communications and computations improves efficiencies [5,9,10].…”

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

“…They studied the same problem using the exponential spectral filter on a N =1500 2 grid. Yin et al 6 also used the same exponential spectral filter in their parallel fast Fourier transform (PFFT) scheme using larger number of grid points . Different dealiasing schemes are implemented with the classical RK4 temporal scheme to test the resolving capability of capturing the sharp density gradient within a unstable bubble using just adequate spatial resolution N =512 2 .…”

“…We will show that numerical results obtained from the RK4‐based RPSM scheme displays lesser parasitic currents. We have used the same initial conditions used in References 6,50 for comparison purposes. The initial conditions for solving the 2D inviscid Boussinesque equations are as follows 6,50 …”

“…We have used the same initial conditions used in References 6,50 for comparison purposes. The initial conditions for solving the 2D inviscid Boussinesque equations are as follows 6,50 where …”

Kolmogorov flow in two dimensional strongly coupled dusty plasma

“…To find out the nonstationary solutions of this nonlinear differential equation, we use here pseudo spectral method. 25 Nordsieck predictor-corrector method has been used for time-stepping. As pseudo spectral method is used here, to avoid the aliasing error, there are several methods which one can use, such as 3 2 -rule, 26 2 ffiffi 2 p 3 -rule, 27 2 3 -rule (zero-padding method).…”