INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2007; 53:1819–1845 Published online 25 October 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fld.1384 Numerical simulation of natural and mixed convection flows by Galerkin-characteristic method Mofdi El-Amrani 1, ∗, † and Mohammed Sea¨ ıd 2 1 Departmento Matem´ aticas, Universidad Rey Juan Carlos, c/Tulip´ an s/n, Mostoles-Madrid 28933, Spain 2 Universit¨ at Kaiserslautern, Fachbereich Mathematik, Kaiserslautern 67663, Germany SUMMARY A numerical investigation is performed to study the solution of natural and mixed convection flows by Galerkin-characteristic method. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization in primitive variables. It can be interpreted as a fractional step technique where convective part and Stokes/Boussinesq part are treated separately. The main feature of the proposed method is that, due to the Lagrangian treatment of convection, the Courant–Friedrichs– Lewy (CFL) restriction is relaxed and the time truncation errors are reduced in the Stokes/Boussinesq part. Numerical simulations are carried out for a natural convection in squared cavity and for a mixed convection flow past a circular cylinder. The computed results are compared with those obtained using other Eulerian-based Galerkin finite element solvers, which are used for solving many convective flow models. The Galerkin-characteristic method has been found to be feasible and satisfactory. Copyright 2006 John Wiley & Sons, Ltd. Received 20 February 2006; Revised 11 July 2006; Accepted 15 July 2006 KEY WORDS: natural convection; mixed convection; modified method of characteristics; Galerkin finite element method 1. INTRODUCTION Natural and mixed convection flows are encountered in various engineering systems, such as solar thermal receivers, electronic cooling devices, microwave ovens, crystal growth, fire in buildings, etc. The governing equations of fluid flow and heat transfer, in most of these problems, are the incompressible Navier–Stokes/Boussinesq equations. These equations are the subject of very intensive research activities since they include a wide variety of difficulties which typically arise in ∗ Correspondence to: Mofdi El-Amrani, Departmento Matem´ aticas, Universidad Rey Juan Carlos, c/Tulip´ an s/n, Mostoles-Madrid 28933, Spain. † E-mail: mofdi.elamrani@urjc.es Contract/grant sponsor: Universidad Rey Juan Carlos; contract/grant number: GDV-04-3 Copyright 2006 John Wiley & Sons, Ltd.