Abstract
In the framework of the spectral element method, a comparison is carried out on turbulent first-and second-order statistics generated by large eddy simulation (LES), under-resolved (UDNS) and fully resolved direct numerical simulation (DNS). The LES is based on classical models like the dynamic Smagorinsky approach or the approximate deconvolution method. Two test problems are solved: the lid-driven cubical cavity and the differentially heated cavity. With the DNS data as benchmark solutions, it is shown that the numerical results produced by the UDNS calculation are of the same accuracy, even in some cases of better quality, as the LES computations. The conclusion advocates the use of UDNS and calls for improvement of the available algorithms.
Highlights
The numerical simulation of turbulent flows still remains a major challenge, especially at high values of the Reynolds number
The under-resolved DNS (UDNS) was done with a Legendre spectral element code presented in [21], while the direct numerical simulation (DNS) results were produced with a Chebyshev spectral method described in [12] [13]
It is unclear how the accuracy of two different numerical methods can be compared, there is no doubt that the resolution of UDNS1000 is coarser than the one in the DNS
Summary
The numerical simulation of turbulent flows still remains a major challenge, especially at high values of the Reynolds number. The dynamic Smagorinsky model [5] [6] may be chosen and the modal [7] or nodal [8] filters represent one of the basic features of the numerical procedure. This approach was successfully carried out by Blackburn and Schmidt [9] and Bosshard et al [10]. The two DNS test cases are the lid-driven cavity (LDC) problem [11] [12] and the differentially heated cavity (DHC) [13] Both problems were solved by a Chebyshev spectral method with discretizations resolving all spatial scales till the Kolmogorov scale.
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