Feasibility Study of an Adaptive Large Eddy Simulation Method

A novel method for simulating turbulent flows called Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) is introduced. The theoretical basis for SCALES is presented using results from a priori testing of homogenious turbulence along with a novel Coherency Diagram of a turbulent field that physically relates Direct Numerical Simulation to different Large Eddy capturing methods, such as SCALES, CVS, LES and VLES. Results from a priori testing show that given the same compression ratio the SCALES method will result in a significantly lower level of subgrid scale dissipation that needs to be modeled in comparison to LES. The feasiability of SCALES is demonstrated by considering numerical simulations of two dimensional flow around a cylinder for Reynolds numbers in the range 3 × 10 1 ≤ Re ≤ 10 5 using an adaptive wavelet collocation method. It is demonstrated in actual dynamic simulations that the compression scales like Re 1/2 over five orders of magnitude, while computational complexity scales like Re. This represents a significant improvement over the naive complexity estimate of Re 9/4 for two-dimensional turbulence. Introduction The problem of simulating high Reynolds number (Re) turbulent flows of engineering and scientific interest would have essentially been solved with the advent of Direct Numerical Simulation (DNS) techniques if unlimited computing power, memory, and time could be applied to each particular problem. Yet given the current and near future computational resources that exist and a reasonable limit on the amount of time an engineer or scientist can wait for a result, the DNS technique will not be useful for more than unit or benchmark problems for the foreseeable future. 1, 2 The high computational cost for the DNS of three dimensional turbulent flows results from the fact that they have eddies of significant energy in a range of scales from the characteristic length scale of the flow all the way down to the Kolmogorov length scale. Because of the large disparity in scales that need to be fully resolved, the actual cost of doing a three dimensional DNS scales as Re 9/4. Fortunately, because the eddies are localized in space and scale, there is a possibility of " compressing " the problem. This lo-calization can be exploited by locally compressing the problem such that all the modes from the characteristic length scale down to the Kolmogorov length scale are still resolved. This can be achieved by applying a recently developed dynamically adaptive …