Edge‐based data structures for a symmetric stabilized finite element method for the incompressible Navier–Stokes equations with heat transfer

Abstract

AbstractThis work presents a new implementation of the De Sampaio–Coutinho formulation (Int. J. Numer. Meth. Fluids 1999; 29:289–309), a segregated Petrov–Galerkin/generalized least‐squares method, for the solution of the incompressible Navier–Stokes equations with heat transfer. Such a formulation produces symmetric, positive‐definite matrices, allowing the use of a preconditioned conjugate gradient solver for each unknown. The formulation also intrinsically introduces streamline upwinding by the choice of adequate time steps, providing a suitable description of convective dominated flows. The code was primarily written using element‐based data structures, making use of parallel/vector techniques and mesh adaptivity. However, schemes based on edge‐based data structures have been introduced with the aim of reducing flop count, memory demands and indirect addressing. In this work, the De Sampaio–Coutinho formulation has been re‐written considering an edge‐based arrangement. The effectiveness of the new scheme was observed solving some standard test cases, as shown in this paper, with a comparatively high gain in computational efficiency. Copyright © 2006 John Wiley & Sons, Ltd.