Eventos Anais de eventos
ENCIT 2018
Brazilian Congress of Thermal Sciences and Engineering
STUDY OF PARAMETERS OF THE MULTIGRID METHOD FOR THE SOLUTION OF 2D HEAT DIFFUSION PROBLEM USING NON-ORTHOGONAL STRUCTURED GRIDS
Submission Author:
Daiane Zanatta , PR
Co-Authors:
Daiane Zanatta, Luciano Araki, Marcio Pinto, Diego Fernando Moro
Presenter: Daiane Zanatta
doi://10.26678/ABCM.ENCIT2018.CIT18-0116
Abstract
The purpose of this work was to study the behavior of the geometric multigrid method on the CPU time for a two-dimensional linear heat diffusion problem, governed by Poisson equation, with Dirichlet boundary conditions in a trapezoidal geometry. For this, two grid generation methods were used to generate the non-orthogonal structured grids. In the first method, algebraic method, Lagrange interpolation was used. The second one was based on solving a system of Laplace equations. The considered parameters that were assessed in order to reduce the CPU time are: number of inner iterations of the solver (ν), number of grids (L) and number of unknowns (N) . The differential equation was discretized by the finite volume method (FVM) and two-dimensional uniform grid in each direction, with second order approximation scheme (CDS). The Dirichlet type boundary conditions were applied through ghost cell method. The system of algebraic equations was solved using lexicographical Gauss-Seidel smoothing. In order to accelerate the convergence of the iterative scheme, the multigrid method with Correction Scheme, V-cycle and coarsening ratio r = 2 was used. Results show that: νoptimum = 2 or 3 for grids generated by employing Lagrange interpolation and νoptimum = 2 or 4 for grids generated by employing differential equations; Loptimum = Lmax usually presents the lowest values of time CPU; the orders of complexity of the algorithm for with grids generated by employing Lagrange interpolation as well as a system of differential equations for the multigrid method are p = 1.116 and p = 1.073, respectively, which is inaccordance with the theoretical efficiency of the multigrid method.
Keywords
CFD, geometric multigrid, Finite volume method, non-orthogonal grids
