MULTIGRID NUMERICAL SOLUTIONS OF LAMINAR BACK STEP FLOW Maximilian S. Mesquita Marcelo J.S. de Lemos Departamento de Energia - IEME Instituto Tecnológico de Aeronáutica - ITA 12228-900 – São José dos Campos - SP, Brasil - E-mail: delemos@mec.ita.br Abstract. This work investigates the efficiency of the multigrid numerical method when applied to solve the temperature field after a sudden expansion in a channel flow. The numerical method includes finite volume discretization with the flux blended deferred correction scheme on structured orthogonal regular meshes. The correction storage (CS) multigrid algorithm performance is compared for different inlet Reynolds numbers and the number of sweeps in each grid level. Up to four grids for both multigrid V- cycles are considered. Results indicate a better performance of the V-cycle and reduction in computational effort for larger Peclet numbers. Key-words: Sudden Expansion, Multigrid, CFD, Numerical Methods 1. INTRODUCTION Convergence rates of single-grid calculations are greatest in the beginning of the process, slowing down as the iterative process goes on. This effect gets more pronounced as the grid becomes finer. Large grid sizes, however, are often needed when resolving small recirculating regions or detecting high heat transfer spots. The reason for this hard-to-converge behavior is that iterative methods can efficiently smooth out only those Fourier error components of wavelengths smaller than or comparable to the grid size. In contrast, multigrid methods aim at covering a broader range of wavelengths through relaxation on more than one grid. The number of iterations and convergence criterion in each step along consecutive grid levels visited by the algorithm determines the cycling strategy, usually a V- or a W-cycle. Within each cycle, the intermediate solution is relaxed before (pre-) and after (post- smoothing) the transportation of values to coarser (restriction) or to finer (prolongation) grids (Brandt, 1977, Stüben and Trottenberg, 1982, Hackbusch, 1985). Accordingly, multigrid methods can be roughly classified into two major categories. In the CS formulation, algebraic equations are solved for the corrections of the variables whereas, in the full approximation storage (FAS) scheme, the variables themselves are handled in all grid levels. It has been pointed out in the literature that the application of the CS formulation is recommended for the solution of linear problems being the FAS formulation more suitable to non-linear cases (Brandt, 1977, Stüben and Trottenberg, 1982, Hackbusch,