Reynolds number scaling of coherent vortex simulation and stochastic coherent adaptive large eddy simulation

Abstract

In view of the ongoing longtime pursuit of numerical approaches that can capture important flow physics of high Reynolds number flows with fewest degrees of freedom, two important wavelet-based multi-resolution schemes are thoroughly examined, namely, the Coherent Vortex Simulation (CVS) and the Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) with constant and spatially/temporarily variable thresholding. Reynolds number scaling of active spatial modes for CVS and SCALES of linearly forced homogeneous turbulence at high Reynolds numbers is investigated in dynamic study for the first time. This dynamic computational complexity study demonstrates that wavelet-based methods can capture flow-physics while using substantially fewer degrees of freedom than both direct numerical simulation and marginally resolved LES with the same level of fidelity or turbulence resolution, defined as ratio of subgrid scale and the total dissipations. The study provides four important observations: (1) the linear Reynolds number scaling of energy containing structures at a fixed level of kinetic energy, (2) small, close to unity, fractal dimension for constant-threshold CVS and SCALES simulations, (3) constant, close to two, fractal dimension for constant-dissipation SCALES that is insensitive to the level of fidelity, and (4) faster than quadratic decay of the compression ratio as a function of turbulence resolution. The very promising slope for Reynolds number scaling of CVS and SCALES demonstrates the potential of the wavelet-based methodologies for hierarchical multiscale space/time adaptive variable fidelity simulations of high Reynolds number turbulent flows.

Wavelet-based adaptive large-eddy simulation of supersonic channel flow

“…Predictably, the WA-LES approach becomes more and more effective with increasing Reynolds number. Further research, similar to what was performed in Kevlahan, Alam & Vasilyev (2007) and Nejadmalayeri, Vezolainen & Vasilyev (2013) for homogeneous isotropic turbulence, will be required to fully characterize the Reynolds-number scaling of the proposed methodology for high-speed compressible flows.…”

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

“…In principle, a very low but non-zero value for this parameter can be prescribed so that the effect of unresolved motions can be completely ignored and the direct solution of the governing equations (2.2) is provided. Even though the number of degrees of freedom is strongly reduced compared with non-adaptive DNS, and the Reynolds number scaling improves with respect to conventional estimates (Nejadmalayeri, Vezolainen & Vasilyev 2013), the WDNS approach still remains unaffordable, even at moderately high Reynolds numbers.…”

Wavelet-based adaptive simulations of three-dimensional flow past a square cylinder

“…In principle, a very low but non-zero value for this parameter can be prescribed so that the effect of unresolved motions can be completely ignored and the wavelet-based direct numerical solution of the penalized equation (2.5) is carried out, whereũ i ∼ =ũ > i . Even though the number of degrees-of-freedom of the WDNS is strongly reduced compared to non-adaptive DNS and the Reynolds number scaling is improved compared with conventional estimates (Kevlahan, Alam & Vasilyev 2007;Nejadmalayeri, Vezolainen & Vasilyev 2013), the computational cost still remains very high even at moderately large Reynolds number, thus, necessitating the use of turbulence modelling approaches.…”