Fully adaptive turbulence simulations based on Lagrangian spatio-temporally varying wavelet thresholding

Abstract

A new framework for spatio-temporally adaptive turbulence simulations is proposed. The method is based on a variable-fidelity representation that tightly integrates numerics and modelling of subgrid-scale turbulence and aims to capture the flow physics on a near-optimal adaptive mesh. The integration is achieved by combining hierarchical wavelet-based computational modelling with spatially and temporally varying wavelet threshold filtering. The proposed approach provides automatic smooth transition from directly resolving all flow physics to capturing only the energetic/coherent structures, which leads to a dynamically adaptive variable-fidelity approach. The self-regulating continuous switch between different fidelity regimes is accomplished through a two-way feedback mechanism between the modelled dissipation and the local grid resolution, which is based on spatio-temporal variation of the wavelet filtering threshold. The proposed methodology systematically accounts for and exploits the spatial and temporal intermittency of turbulence. Thus, it overcomes the major limitation of all existing wavelet-based multi-resolution techniques, namely, the use of a global thresholding criterion. The procedure consists of tracking the wavelet thresholding factor within a Lagrangian frame by exploiting a Lagrangian path-line diffusive averaging approach, based on either interpolation along characteristics or direct solution of the corresponding evolution equation. This new methodology is tested for linearly forced homogeneous turbulence at different Reynolds numbers and provides very promising results on a benchmark with time-varying prescribed level of turbulence resolution.

Wall-resolved wavelet-based adaptive large-eddy simulation of bluff-body flows with variable thresholding

“…As empirically demonstrated, the initial sharp discontinuity existing at the inlet boundary does not introduce any significant difficulties in the subsequent evolution of the threshold field and correctly disappears afterwards. Finally, in order to achieve a sufficiently smooth threshold field, the artificial diffusion coefficient in the Lagrangian path-line diffusive approach is set to C ν = 0.1, which is one of the optimal values suggested in Nejadmalayeri et al (2014), where a systematic study on the influence of this parameter was performed.…”

“…A more general variable thresholding formulation that includes spatial variation was recently considered and demonstrated for homogeneous isotropic turbulence by Nejadmalayeri et al (2014). In the present work, the spatio-temporally varying thresholding is extended to wall-bounded flows, while formalizing the approach in the framework of the Lagrangian path-line diffusive averaging methodology ).…”

“…The viscosity-like coefficient ν for the artificial diffusion term is determined by imposing that the diffusion time scale ∆ 2 /ν is comparable to the local time scale |S > | −1 . This leads to utilizing the classical Smagorinsky-like scaling for this parameter, namely, ν (x, t) = C ν ∆ 2 |S > |, where C ν is a dimensionless coefficient of order unity (Nejadmalayeri et al 2014).…”

“…The robustness of the wavelet-based approach to homogeneous turbulence simulation has been further improved by introducing the physics-based spatio-temporally variable thresholding strategy. The method adjusts the wavelet threshold to achieve spatially uniform turbulence resolution and fully exploits the intermittency of turbulence by solving a Lagrangian evolution equation for the threshold field (Nejadmalayeri et al 2014).…”

Parallel adaptive wavelet collocation method for PDEs

“…Adaptive Wavelet Collocation Method (AWCM) is such a technique, which has been developed and thoroughly investigated for parabolic [1,2], hyperbolic [3], and elliptic [4] partial differential equations. It was successfully applied to a wide spectrum of problems including incompressible [5], compressible subsonic [6] and supersonic [3] flows, wavelet-based Adaptive Large Eddy Simulation [7,8,9,10,11,12,13], thermoacoustic wave propagation [14], Rayleigh-Taylor instability [15], ocean modeling [16], combustion [17], fluid-structure interactions [18,19], viscoelastic and poroviscoelastic flows [20,21,22].…”