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Edge‐based data structures for a symmetric stabilized finite element method for the incompressible Navier–Stokes equations with heat transfer
Author(s) -
Kraft R. A.,
Coutinho A. L. G. A.,
de Sampaio P. A. B.
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1372
Subject(s) - solver , finite element method , mathematics , compressibility , conjugate gradient method , computer science , mesh generation , mathematical optimization , engineering , aerospace engineering , structural engineering
This 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.