Deconvolution of induced spatial discretization filters subgrid modeling in LES: application to two-dimensional turbulence

Abstract

The paper presents a new approximate deconvolution subgrid model for Large Eddy Simulation in which corrections to implicit filtering due to spatial discretization are integrated explicitly. The top-hat filter implied by second-order central finite differencing is a key example, which is discretised using the discrete Fourier transform involving all the mesh points in the computational domain. This discrete filter kernel is inverted by inverse Wiener filtering. The inverse filter obtained in this way is used to deconvolve the resolved scales of the implicitly filtered velocity field on the computational grid. Subgrid stresses are subsequently calculated directly from the deconvolved velocity field. The model was applied to study decaying two-dimensional turbulence. Results were compared with predictions based on the Smagorinsky model and the dynamic Germano model. A posteriori testing in which Large Eddy Simulation is compared with filtered Direct Numerical Simulation obtained with a Fourier spectral method is included. The new model presented strictly speaking applies to periodic problems. The idea of recovering a high-order inversion of the numerically induced filter kernel can be extended to more general non-periodic problems, also in three spatial dimensions.