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COBEM 2019
25th International Congress of Mechanical Engineering
NUMERICAL EFFICIENCY AND VERIFICATION OF AN IMPLICIT SOLVER TO COMPUTE HEAT TRANSFER PROBLEMS
Submission Author:
Tobias Luiz Marchioro Toassi , PR , Brazil
Co-Authors:
Tobias Luiz Marchioro Toassi, Francisco Augusto Aparecido Gomes, Paulo Gemo Conci
Presenter: Tobias Luiz Marchioro Toassi
doi://10.26678/ABCM.COBEM2019.COB2019-1522
Abstract
In this paper we aim to study the efficiency and accuracy of Generalized Minimal Residual (GMRES), one of the most effective iterative methods for solving large sparse linear system of equations and a family of preconditioners (ILU) to solve pure diffusive problems. Two cases are going to be analyzed, a rectangular domain subject to a steady heat conduction problem, and a unitary square domain subject to a transient problem. For the discretization was utilized the finite difference method, that consists by replacing the derivatives in the differential equations by finite difference approximations. A fully implicit scheme was utilized on the transient analysis, so it could eliminate the stability condition problem that occur on explicit schemes, as in these cases the maximum value of $\Delta t$ is defined by the largest eigenvalue of the differential equation over the analyzed mesh, a reduction in the amount of computation time may often be realized by employing an implicit, rather than explicit, finite difference scheme. When applied to several meshes, it was possible to analyze the rate of convergence or order of discretization, the results were compatible with the expected order. The GMRES presented several advantages over the others iterative methods, such as Gauss-Siedel, and was even more efficient when the linear system was preconditioned.
Keywords
Finite Difference Method, GMRES, Numerical analysis, Diffusive Problems
