MULTIGRID METHOD FOR THE SOLUTION OF 2D HEAT DIFFUSION PROBLEM USING NON-ORTHOGONAL STRUCTURED GRIDS
Daiane Cristina Zanatta1; Luciano Kiyoshi Araki2; Marcio Augusto Villela Pinto2
1 State University of Centro-Oeste, Irati-PR, Brazil.; 2 Federal University of Paraná, Curitiba - PR, Brazil.
doi:10.20906/CPS/CILAMCE2017-0176
Resumo
The purpose of this work is the study the behavior of the geometric multigrid method on the CPU time for a two-dimensional problem of interest of Computational Fluid Dynamics (CFD). The mathematical problem considered is related to the two-dimensional linear heat conduction problem, governed by Poisson equation, with Dirichlet boundary conditions in an L-shaped geometry. For the generation of structured non-orthogonal meshes was used the algebraic method that employs Lagrange interpolation. The analysis was done using a comparative between singlegrid and multigrid, dimensionless residual drop, CPU time and number of V-cycles. The differential equation is discretized by the finite volume method (FVM) with second order approximation scheme. The Dirichlet type boundary conditions are applied through ghost volume technique. The systems of algebraic equations are solved using the Gauss-Seidel solver. In order to accelerate the convergence of the iterative scheme, the multigrid method with Full Approximation Scheme (FAS), V-cycle and coarsening ratio r = 2 was used.
Palavras-chave: CFD; Geometric multigrid; Finite volume method; Non-orthogonal grids