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

El-Amrani, M.; Seaid, M.

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.

Citation

El-Amrani, M., & Seaid, M. (2008). A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer. SIAM Journal on Scientific Computing, 30(6), 2734-2754. https://doi.org/10.1137/080720711

• Journal Article Type: Article
• Acceptance Date: Jun 26, 2008
• Online Publication Date: Oct 13, 2008
• Publication Date: Oct 13, 2008
• Deposit Date: Mar 20, 2018
• Publicly Available Date: Mar 20, 2018
• Journal: SIAM Journal on Scientific Computing
• Print ISSN: 1064-8275
• Electronic ISSN: 1095-7197
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 6
• Pages: 2734-2754
• DOI: https://doi.org/10.1137/080720711
• Keywords: Galerkin-characteristic method, Large-eddy simulation, Heat transfer, Finite element method, Mixed convection, Sea-surface temperature
• Public URL: https://durham-repository.worktribe.com/output/1528675