Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 59, Issue 1 (2019) 1-12 1 Journal of Advanced Research in Fluid Mechanics and Thermal Sciences Journal homepage: www.akademiabaru.com/arfmts.html ISSN: 2289-7879 CVFEM coupled with FLO Scheme for Solution to Heat and Fluid Problems Mostefa Kaouari 1, , Fodil Hammadi 2 , Belkacem Draoui 3 1 Laboratory of Mechanics: Simulation & Experimentation (L2ME), Algeria 2 TAHRI Mohamed University of Bechar, Algeria 3 ENERGARID Laboratory, TAHRI Mohamed University of Bechar, Algeria ARTICLE INFO ABSTRACT Article history: Received 11 September 2018 Received in revised form 3 February 2019 Accepted 12 May 2019 Available online 15 July 2019 Nowadays, CVFEM has proved to be an effective method for solving real problems in CFD. Combining advantages of CVFDMs with those of FEMs results in an improved method, able to deal with complexes geometries, and satisfy local and global conservation principles. To solve dynamical field, a good scheme is always required for discretization of the convective terms. The FLO scheme is opted for in this study, because it is extracted as exact solution from a modified equation. The resolution procedure used is the SIVA. Coding this procedure is achieved using advanced instructions in Fortran 90/95. The presented results, prove a best agreement with benchmarks. Keywords: CVFE; FLO scheme; SIVA; Fortran 90/95 Copyright © 2019 PENERBIT AKADEMIA BARU - All rights reserved 1. Introduction Control Volume Finite Element Method (CVFEM) is increasingly used in solving fluid flow and heat transfer problems of different complexities. The success reached in merging the two ancient methods in CFD problems (i.e. CVFDM and FEM), increased the field of application CVFEM method. The physical domain is discretized in three nodes triangular elements; every element is subsequently divided in three sub-volumes; this geometrical treatment is achieved by collecting all sub-volumes surrounding the considered node to construct the control volume. In addition, other geometrical information is required in the phase of discretization of conservation and continuity equations. Convective terms present in the momentum equations are very difficult to handle it without specific considerations. These convective terms are approximated by interpolation function that responds to an element Peclet number and take into account the direction of the element average velocity vector. The diffusive terms are interpolated linearly, and there is no reason to use the same scheme used for convective ones. The first eminent work that presents the FLO scheme is Baliga and Patankar [1, 2], the ideas behind this scheme was proposed in the work of Raithby [3-5].  Corresponding author. Email address: Kaouari_must@yahoo.fr (Mostefa Kaouari) Open Access