Successive inverse polynomial interpolation to optimize Smagorinsky's model for large-eddy simulation of homogeneous turbulence

We propose the successive inverse polynomial interpolation method to optimize model parameters in subgrid parameterization for large-eddy simulation. This approach is illustrated for the Smagorinsky eddy-viscosity model used in homogeneous decaying turbulence. The optimal Smagorinsky parameter is resolution dependent and provides minimal total error in the resolved kinetic energy. It is approximated by starting with a “bracketing interval��? that is obtained from separate “no-model��? and “dynamic eddy-viscosity��? large-eddy simulations. The total error level is reduced 3–6 times compared to the maximal initial errors. The computational overhead of the full optimization at resolution N3 is comparable to a single simulation at $(3N/2)^3$ grid cells. The increased accuracy is higher than obtained with dynamic modeling at a resolution of $(4N)^3$.