A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 April 2014
Issue publication date: 1 April 2014
Abstract
Purpose
The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems.
Design/methodology/approach
The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error.
Findings
Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity.
Originality/value
The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.
Keywords
Acknowledgements
This work was done during a stay of the first author at the Public Research Center Henri Tudor at Luxembourg and has been supported by the National Research Funding of Luxembourg (FNR) via Accompanying Measure AM2c program, FNR/11/AM2c/16. Part of this research work has been achieved in the framework of the FNR CORE OMIDEF project (FNR/786643).
Citation
Younes, A., Makradi, A., Zidane, A., Shao, Q. and Bouhala, L. (2014), "A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 3, pp. 735-759. https://doi.org/10.1108/HFF-07-2012-0156
Publisher
:Emerald Group Publishing Limited
Copyright © 2014, Emerald Group Publishing Limited