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Symmetry-preserving regularization of wall-bounded turbulent flows
Trias Miquel, Francesc Xavier; Gorobets, Andrei; Verstappen, R.W.C.P.; Oliva Llena, Asensio
Universitat Politècnica de Catalunya. Departament de Màquines i Motors Tèrmics; Universitat Politècnica de Catalunya. CTTC - Centre Tecnològic de la Transferència de Calor
The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces an hyper-viscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. To do so, a new criterion based on the invariants of the local strain tensor is proposed here. Altogether, the proposed method constitutes a parameter-free turbulence model.
Peer Reviewed
Àrees temàtiques de la UPC::Física::Termodinàmica::Física de la transmissió de la calor
Turbulent convective heat transfer
Navier-Stokes equations
Turbulències -- Simulació numèrica
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