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Spectrally-consistent regularization modeling at very high Rayleigh numbers

DOI: 10.1615/ICHMT.2012.ProcSevIntSympTurbHeatTransfPal.1230
pages 1189-1200

F. Xavier Trias
Heat and Mass Transfer Technological Center (CTTC) Universitat Politecnica de Catalunya - BarcelonaTech (UPC) Colom 11, 08222 Terrassa, Barcelona, Spain; and Institute of Mathematics and Computing Science, University of Groningen, The Netherland

Andrey Gorobets
Heat and Mass Transfer Technological Center, Technical University of Catalonia ETSEIAT, C/Colom 11, 08222 Terrassa, Spain; Keldysh Institute of Applied Mathematics, 4A, Miusskaya Sq., Moscow 125047, Russia

R.W.C.P. Verstappen
Institute of Mathematics and Computing Science, University of Groningen P.O. Box 407, 9700 AK Groningen, The Netherlands

Assensi Oliva
Centre Tecnologic de Transferencia de Calor (CTTC), Universitat Politecnica de Catalunya (UPC), Colom 11, 08222 Terrassa, Barcelona, Spain


The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Rayleigh 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 a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a selfadjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. The performance of the novel regularization modeling approach is assessed through application to turbulent natural convection flows at very high Rayleigh numbers.

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