On the Control of the Mass Errors in Finite Volume-Based Approximate Projection Methods for Large Eddy Simulations

What does Finite Volume-based implicit filtering really resolve in Large-Eddy Simulations?

“…Owing both to the specific flux decomposition [15,17,42] and to the numerical character of the unresolved tensor stress [8,16,18,21,24,25], the use of the integral-based LES equation (8) affects also the choice of the SGS modeling. The velocity v d is now representative of a finite-dimensional state-vector, possessing only a finite numbers of resolved length scales, bounded by the smallest computational size associated with the Nyquist frequency h/p.…”

“…We will never need to discretize the divergence operator but only the integral of the flux [11][12][13][14][15]17]. Thus, one writes the integral equation…”

“…A new integral-based SGS dynamic procedure has been introduced consequently, which enables the Germano identity to be properly rewritten, and the multi-dimensional character of the model constant to be preserved, see Refs. [14,15,17,42].…”

“…In fact, Q = 1-2 typically results in implicit FV-based filtering LES and closure modeling also contains important contributions which are sensitive to the adopted spatial discretization [24]. Thus, discretizations of the filtered equations and the resulting numerical errors (local truncation error, aliasing) have been analyzed in many papers [8,13,15,16,18,[20][21][22][23][24][25]28], although the conclusions drawn are not always consistent. The relevance of using FV-based LES equations has been marginally highlighted in recently published papers, e.g.…”

“…[11,12]), the ''FV method'' is referred to here as a discretization of the integral conservation laws 1 (see also Refs. [13][14][15]40]). Accordingly, any type of numerical flux reconstruction always drive to update the discrete cell-variable that results in a unique approximation 2 of the top-hat filtered variable (which is a smooth filtering in wavenumber space [27]), associated with the local volume average over a small domain of linear measure D, e.g.…”