A new development of the dynamic procedure for the integral-based implicit filtering in large-eddy simulation

This paper is focused on the role of integral-based Finite Volume (FV) discretizations in Large Eddy Simulation of turbulence. The integral-based form implicitly induces the top-hat filtering on the balanced variable. This leads us to rewrite also a different decomposition of the fluxes. As a consequence, the development of a new Germano identity can be achieved having some advantages over the classical differential-based form. However, the dynamic procedure requires an explicit test-filtering on a computational grid that, to be optimal, requires an evaluation of the shape of the numerical filter induced by the FV-based discretization. Therefore, the goal of this paper is the theoretical study of the effective filter shape induced by some 3D Finite Volume reconstructions. The induced shape and width are analyzed by means of a modified wavenumber-like analysis that is applied in the 3D Fourier space. Some schemes are considered and the differences in terms of either velocity or flux interpolations on either staggered or non-staggered grids are derived and analyzed.