High-order methods for decaying two-dimensional homogeneous isotropic turbulence

Abstract

Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is investigated for direct numerical simulations (DNS) of homogeneous isotropic two-dimensional decaying turbulent flows. The numerical accuracy of compact difference, explicit central difference, Arakawa, and dispersion-relation-preserving schemes are analyzed and compared with the Fourier-Galerkin pseudospectral scheme. In addition, several explicit Runge-Kutta schemes for time integration are investigated. We demonstrate that the centered schemes suffer from spurious Nyquist signals that are generated almost instantaneously and propagate into much of the field when the numerical resolution is insufficient. We further show that the order of the scheme becomes increasingly important for increasing cell Reynolds number. Surprisingly, the sixth-order schemes are found to be in perfect agreement with the pseudospectral method. Considerable reduction in computational time compared to the pseudospectral method is also reported in favor of the finite difference schemes. Among the fourth-order schemes, the compact scheme provides better accuracy than the others for fully resolved computations. The fourth-order Arakawa scheme provides more accurate results for under-resolved computations, however, due to its conservation properties. Our results show that, contrary to conventional wisdom, difference methods demonstrate superior performance in terms of accuracy and efficiency for fully resolved DNS computations of the complex flows considered here. For under-resolved simulations, however, the choice of difference method should be made with care.

References in corpus (4)

• An update on the double cascade scenario in two-dimensional turbulence
• Computational aspects of astrophysical MHD and turbulence
• Approximate deconvolution large eddy simulation of a barotropic ocean circulation model
• Experimental Study of Energy Transfer by Inertial Waves During the Build up of Turbulence in a Rotating System

Cited by in corpus (19)

• Sub-grid modelling for two-dimensional turbulence using neural networks
• A neural network approach for the blind deconvolution of turbulent flows
• Sub-grid scale model classification and blending through deep learning
• Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors
• Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons
• A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation
• Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model
• Memory embedded non-intrusive reduced order modeling of non-ergodic flows
• Divergence-free $H$(div)-FEM for time-dependent incompressible flows with applications to high Reynolds number vortex dynamics
• A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
• A posteriori analysis of low-pass spatial filters for approximate deconvolution large eddy simulations of homogeneous incompressible flows
• Evaluation of explicit and implicit LES closures for Burgers turbulence
• Frame invariant neural network closures for Kraichnan turbulence
• Discretize first, filter next: learning divergence-consistent closure models for large-eddy simulation
• Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration
• Stationary two-dimensional turbulence statistics using a Markovian forcing scheme
• Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction
• A new data-driven energy-stable Evolve-Filter-Relax model for turbulent flow simulation
• Generalized deconvolution procedure for structural modeling of turbulence