A two-dimensional schematic of the filtered-boundary formulation for a general flow domain with a boundary given by , which includes both walls and inflow/outflow/free-stream boundaries. A buffer region (shaded), where is imposed, is appended to the flow domain. The filtered velocity is computed by integrating the filter kernel over the extended domain . The empty circles indicate the set of collocation points of any filtered function inside the flow domain , and the filled circles indicate the set of collocation points inside the buffer domain .
(a) Mean velocity and (b) rms streamwise velocity of turbulent channel flow for , filtered-boundary simulation (—) and DNS (– – –).
(a) Target streamwise mean velocity profiles and (b) rms values prescribed by the NL boundary condition, in which the velocity field is 0 inside the buffer and the MB boundary condition, in which the velocity field is inside the buffer, compared to the original filtered mean and rms velocity profiles from DNS of turbulent channel flow. Details of the filter and the channel domain are the same as that described in Sec. IV.
Schematic of the channel flow with buffer regions added in the wall-normal direction on both sides. The velocity field in this extended domain is subjected to a Fourier cutoff filter in all three directions.
Effect of the boundary terms on the evolution of a Tollmien–Schlichting wave in a channel flow. Shown are (a) filtered velocity, (b) filtered velocity, (c) filtered pressure, (d) pressure gradient, (e) boundary term for equation, and (f) pressure gradient () boundary term. () Real part and (– – –) imaginary part.
Comparison of filtered DNS (—) data with OLES (– – –) simulation performed using the filtered-boundary approach. Profiles are shown for (a) mean streamwise velocity, (b) rms streamwise velocity, (c) rms wall-normal velocity, and (d) rms spanwise velocity. Here, is the distance from the wall.
One-dimensional streamwise [(a) and (c)] and spanwise [(b) and (d)] spectra; filtered DNS (—) and OLES with NL boundary condition (– – –). Here, is the distance from the wall.
Subgrid energy transfer in turbulent channel flow as measured in DNS (Ref. 28). (a) Without wall-normal filtering; total energy transfer , subgrid dissipation , and subgrid transport . (b) Total subgrid energy transfers with and without wall-normal filtering and a posteriori from the filtered-wall LES. Here, is the distance from the wall.
Average dissipation rate in the channel due to [(a), (c), and (e)] wall stresses and [(b), (d), and (f)] subgrid forces from filtered DNS (—) and LES (– – –). Here, is the distance from the wall.
Spectra of for (first row) , (second row) , and (third row) at the wall computed from (first column) DNS and (second column) NL boundary condition.
Comparison of filtered DNS data (—) with the results of LES using the NL boundary condition and OLES with (– – –), OLES with , and OLES with or dynamic Smagorinsky . Profiles are shown for (a) mean streamwise velocity, (b) rms streamwise velocity, (c) rms wall-normal velocity, and (d) rms spanwise velocity. Here, is the distance from the wall.
Values of (time averaged) obtained from different OLES kernels using the MB boundary condition. for DNS.
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