本篇研究利用全顯示多塊網格解穩態與非穩態不可壓縮流.此篇研究求解器是利用人工壓縮網格結合壓力以及速度方程式
對於此求解器是在交錯網格上和collocated grids利用二維及三維上板驅動方腔流體. 此研究利用中央差芬去離散形成交錯網格.以及利用全顯示的MacCormack 在 collocated 網格上
對於上板驅動方腔內流動是測試穩態解Navier-Stokes equation
而 Talyor-Green vortex 還有 Oscillating 是測試非穩態解
本篇研究的主旨是加速求解收斂速度.並根據multi-grid methods利用pseudo-compressibility. 因此. 一個非線性的multi-grid method .通常較FAS方法
對於二維和三維問題.可分別加快到217倍和70倍 加速的速度是取決於multigrid 的大小.然而 隨著雷諾數或者參數變多都將會導致收斂速度變慢

This study focuses on the explicit multigrid solutions of steady and unsteady incompressible flows. An artificial compressibility based solver is adopted to couple the pressure and velocity in governing equations. This solver is validated for two and three-dimensional steady flows on staggered as well as on the collocated grids. The staggered-grid version employs a central-differencing based discretization while the explicit MacCormack scheme is used on the collocated grids. Lid-driven cavity flow is used as a test case for the steady Navier-Stokes equations while decaying Taylor-Green vortex and oscillating lid-driven cavity flow comprises the test cases for unsteady flows. A dual-time stepping within every physical time-step is used for time-accurate results for unsteady test cases.

One of the primary aims of the present work is to accelerate the numerical convergence of this pseudo-compressibility based solver using multigrid methods. Therefore, a non-linear multigrid method, usually called as the full approximation storage (FAS) scheme is implemented on a grid-hierarchy. Multigrid solutions are obtained using up to four grid levels. Accelerations of up to 217 times and 70 times are reported for two and three-dimensional test cases respectively. It has been observed that these accelerations increase with the grid size; however, decrease with the increase in Reynolds number and are parameter dependent.

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