A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. This work aims at the development of a nonoscillatory Galerkin-characteristic method for large-eddy simulation of turbulent flow and heat transfer. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization of the incompressible Navier-Stokes/Boussinesq equations in primitive variables. It can be interpreted as a fractional step technique where the convective part and the Stokes/Boussinesq part are treated separately. A limiting procedure is implemented for the reconstruction of numerical solutions at the departure points. The main feature of the proposed Galerkin-characteristic method is that, due to the Lagrangian treatment of convection, the standard Courant-Friedrichs-Levy condition is relaxed, and the time truncation errors are reduced in the Stokes/Boussinesq part. To solve the generalized Stokes/Boussinesq problem we implement a conjugate gradient algorithm. This method avoids projection techniques and does not require any special correction for the pressure. We verify the method for an advection-diffusion equation with a known analytical solution and for the benchmark problem of mixed convection flow in a squared cavity. We also present numerical results for a problem of heat transport in the Strait of Gibraltar. The Galerkin-characteristic method has been found to be feasible and satisfactory.Key words. Galerkin-characteristic method, large-eddy simulation, heat transfer, finite element method, mixed convection, sea-surface temperature AMS subject classifications. 76F35, 74S05, 65M25DOI. 10.1137/080720711 1. Introduction. The large-eddy simulation (LES) equations for incompressible thermal flows are obtained by applying a spatial filtering to the Navier-Stokes equations subject to the Boussinesq approximation; see [5,4,17,23,16,12] and the references therein. However, this procedure introduces a term called a subgrid stress tensor which needs to be modelled. This term has to be seen as the interaction between the large and small scales in the system. In the current study, we will concentrate on a subgrid problem based on the Smagorinsky model [27]. The LES is normally performed on grids that are just fine enough to resolve the large flow scales, and numerical errors on such grids can have large effects on the simulation results. Although in the literature (see [12] and references therein) many numerical schemes have been presented, it is still not clear what the effect of the numerical and modelling errors in...

A finite element semi‐Lagrangian method with L2 interpolation

“…Furthermore, the SLAG method offers the possibility of using time steps that exceed those permitted by the Courant-Friedrichs-Lewy (CFL) stability condition in Eulerian-based methods for convection-dominated flows. A class of SLAG methods has been investigated in references [5][6][7][10][11][12], among others. The authors in [13] have analyzed a SLAG method for the incompressible Navier-Stokes equations in the finite element framework.…”