Conjugate Gradients in a Computational Fluid Dynamics Problem Applied to Solar Collectors

Abstract

A recurrent drawback when solving heat conduction problems, both with and without sources, is that the convergence linear solvers becomes slow when the state is "stiff". The motivation for this work comes from the simulation of solar collectors, where abrupt variations in conductivity and the formation of hot spots make the problem particularly stiff. A Finite Volume Method code implemented in GNU Octave is used. In this work, the Conjugate Gradient method is applied for the numerical resolution of the algebraic system, and it is compared with the standard direct Cholesky method. In addition, the methods to be compared are described in more detail, and results on accuracy, convergence, and efficiency are presented with different variants of these projection-based methods, analyzing which of them can accelerate convergence, and examining certain characteristics of the assembled matrix, such as conditioning.