| Summary: | 碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 94 === There is urgent need in improving computational efficiency in order to solve fluid flow problems of increasing geometrical complexities. While calculating complicated fluid flow problem, it always needs to use plenty of grid nodes. Because the memory capacity of computer is still limited, it restricts the computational number of grids that can be used. Moreover, iterations on single-grid method increase as increasing of grid nodes and take excessive computation time. Multigrid method is considered as an effective method to enhance the computational speed.
Natural convection in square cavity heated by sidewall is simulated in this study. The governing equations are solved with fractional time-step method, and multigrid method is applied to solve the poisson equation. The test grid meshes are from 64x64 to 256x256. The test levels are from one to four levels, while the multigrid V-cycles are from one to two cycles. The Rayleigh number of the fluid flow is 1x108. Influence of acceleration efficiency with different multigrid levels under different grid meshes is investigated. It also compares the influence of acceleration efficiency with different multigrid cycles under different grid meshes.
According to the present results, it is obviously found that the efficiency of speed-up by using multigrid method increase as increasing of grid nodes. With the increasing levels and cycles of the multigrid method, it can not only enhance the convergence rate but also decrease number of iterations and computation time. The levels and cycles of multigrid should make an adjustment in number of grids, otherwise it will cost more time in the interpolation procedure. The results show that multigrid method is indeed an effective method to accelerate calculation process.
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