Abstract
Abstract. Aliasing errors arise in the multiplication of partial sums, such as those encountered when numerically solving the Navier–Stokes equations, and can be detrimental to the accuracy of a numerical solution. In this work, a performance and cost analysis is proposed for widely used dealiasing schemes in large-eddy simulation, focusing on a neutrally stratified, pressure-driven atmospheric boundary-layer flow. Specifically, the exact 3∕2 rule, the Fourier truncation method, and a high-order Fourier smoothing method are intercompared. Tests are performed within a newly developed mixed pseudo-spectral finite differences large-eddy simulation code, parallelized using a two-dimensional pencil decomposition. A series of simulations are performed at varying resolution, and key flow statistics are intercompared among the considered runs and dealiasing schemes. The three dealiasing methods compare well in terms of first- and second-order statistics for the considered cases, with modest local departures that decrease as the grid stencil is reduced. Computed velocity spectra using the 3∕2 rule and the FS method are in good agreement, whereas the FT method yields a spurious energy redistribution across wavenumbers that compromises both the energy-containing and inertial sublayer trends. The main advantage of the FS and FT methods when compared to the 3∕2 rule is a notable reduction in computational cost, with larger savings as the resolution is increased (15 % for a resolution of 1283, up to a theoretical 30 % for a resolution of 20483).
Highlights
The past decades have seen significant progress in computer hardware in remarkable agreement with Moore’s law, which states that the number of nodes in the discretization grids doubles every 18 months (Moore, 1965; Voller and PortéAgel, 2002; Takahashi, 2005)
We provide a cost–benefit analysis and a comparison of turbulent flow statistics for the Fourier truncation (FT) and Fourier smoothing (FS) dealiasing schemes in comparison to the exact 3/2 rule using a set of large-eddy simulation (LES) of fully developed atmospheric boundary layer (ABL)-type flows
The goal of this study is to develop a cost–benefit analysis for the different, already established, dealiasing methods from a computational cost standpoint as well as in terms of accuracy in reproducing turbulent flow characteristics
Summary
The past decades have seen significant progress in computer hardware in remarkable agreement with Moore’s law, which states that the number of nodes in the discretization grids doubles every 18 months (Moore, 1965; Voller and PortéAgel, 2002; Takahashi, 2005). With increasing computer power, the range of scales and applications in computational fluid dynamics (CFD) has significantly broadened, allowing us to describe – at an unprecedented level of detail – complex flow systems such as fluid–structure interaction (Hughes et al, 2005; Bernaschi et al, 2010; Takizawa and Tezduyar, 2011), land–atmosphere exchange of scalars, momentum and mass (Moeng, 1984; Albertson and Parlange, 1999; BouZeid et al, 2004; Calaf et al, 2010; Anderson et al, 2012; Giometto et al, 2016, 2017), weather research and forecasting (Skamarock et al, 2008), micro-fluidics (Wörner, 2012), and canonical wall-bounded flows (Schlatter and Örlü, 2012), to name but a few Despite this progress, highresolution simulations effectively exploiting current hardware and software capabilities (i.e., following Moore’s law). Methods that aim at reducing computational requirements while preserving numerical accuracy are still of great interest
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