Large-eddy simulation of turbulent channel flows with conservative IDO scheme
The resolution of a numerical scheme in both physical and Fourier spaces is one of the most important requirements to calculate turbulent flows. A conservative form of the interpolated differential operator (IDO-CF) scheme is a multi-moment Eulerian scheme in which point values and integrated average values are separately defined in one cell. Since the IDO-CF scheme using high-order interpolation functions is constructed with compact stencils, the boundary conditions are able to be treated as easy as the 2nd-order finite difference method (FDM). It is unique that the first-order spatial derivative of the point value is derived from the interpolation function with 4th-order accuracy and the volume averaged value is based on the exact finite volume formulation, so that the IDO-CF scheme has higher spectral resolution than conventional FDMs with 4th-order accuracy. The computational cost to calculate the first-order spatial derivative with non-uniform grid spacing is one-third of the 4th-order FDM. For a large-eddy simulation (LES), we use the coherent structure model (CSM) in which the model coefficient is locally obtained from a turbulent structure extracted from a second invariant of the velocity gradient tensor, and the model coefficient correctly satisfies asymptotic behaviors to walls. The results of the IDO-CF scheme with the CSM for turbulent channel flows are compared to the FDM with the CSM and dynamic Smagorinsky model as well as the direct numerical simulation (DNS) by Moser et al. Adding the sub-grid scale stress tensor of LES to the IDO-CF scheme improves the profile of the mean velocity in comparison with an implicit eddy viscosity of the IDO-CF upwind scheme. The IDO-CF scheme with the CSM gives better turbulent intensities than conventional FDMs with the same number of grid points. The turbulent statistics calculated by IDO-CF scheme are in good agreement with the DNS at the various values of Reynolds number Re?=180,395, and 590. It is found that the IDO-CF scheme is suitable for the turbulent flow computation and improves the turbulent statistics with compact stencils.
large-eddy simulation ido scheme coherent structure model multi-moment scheme