Filippo Maria Denaro

The development of the dynamic procedure as well as the deeper understanding of the link between filtering, modelling and numerics, allowed Large Eddy Simulation (LES) to make great progresses during the last years. Among several modelling approaches, the scale-similar-based modelling is based on the observation that the smallest resolved scales are the most active in the interaction with the unresolved ones. Owing to the low dissipation introduced by the scale-similar models (SSMs), the coupling with the eddy-viscosity model is often used in the so-called mixed models. Dynamic version of mixed models is historically based on the application of the test-filtering on the differential form of the filtered momentum equation. Such an approach is used for both the one and the two-coefficients mixed models. The use of the differential form of the filtered equations produces the well-known mathematical inconsistence caused by the need to extract arbitrarily the model functions out of filtering. It is known that, along with the eddy viscosity assumption, the magnitude of the Germano identity error (GIE) is strongly influenced. The mathematical inconsistence in the extraction of the dynamic eddy viscosity coefficient was recently superseded by using the new integral-based formulation. However, owing to the intrinsic limits of the Smagorinsky model, also in those results, the GIE is still remarkable therefore, the present paper presents a new formulation to the integral-based dynamic procedure for both one and two-coefficients mixed models (IDMM). The original contributions of the present paper can be summarised: (1) A theoretical analysis comparing the spectral errors for the differential and integral-based SSM, assessing that the errors are less relevant for the integral form; (2) The implementation of one and two parameters IDMM for the simulation of turbulence in a plane channel flow, assessing the reduction of the GIE and the good behaviour of the statistics that are compared with those of the other LES codes used in the LESinItaly project.

SUMMARY: The numerical simulation of turbulence is one of the most challenging tasks in the field of the modern computational science. At present, the most advanced approach is the large eddy simulation (LES) technique wherein a formal separation between resolved (large) and unresolved (small) scales of the motion is in effect by means of a filtering operation applied onto the governing equations. However, LES requires very sophisticated numerical discretizations in terms of both accuracy and efficiency. Often, the modelling of the unresolved subgrid scale terms adds further computational complexities. This paper illustrates the suitability in using software packages for symbolic computation (in the present case, Maple© for helping in the production of subroutines for a new multidimensional, high‐order accurate finite volume‐based LES code. Specifically, it will be detailed how producing, rapidly and efficiently, the routines for computing convective, diffusive as well as subgrid scale modelling fluxes. It is particularly detailed how exploiting the package for differential calculus and linear algebra for the analytical integration of the flux polynomials over the finite volume faces. The structure of the LES code is illustrated, and an accuracy analysis of the local truncation errors is performed comparing the third‐order accurate multidimensional upwind and the classical second‐order centred reconstruction in the wavenumbers space. Then, some numerical results for the turbulent plane channel and some brief points concerning the parallelization issue are addressed. Copyright © 2012 John Wiley & Sons, Ltd.