在多重網格架構下加速求解異重流方程的三維平行計算

Multigrid acceleration of three dimensional lock-exchange gravity current flow simulation in parallel

王晉偉(Chin-Wei Wang)

指導教授 ： 許文翰

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202001632

摘要

本論文採用多重網格架構以改善求解壓力 Poisson 方程的計算效率，在數值方法中，本論文實作在兩種不同網格系統下的多重網格法，並且將此方法推廣到任意階層，同時比較 V 循環以及 Full 循環的計算效率。此外，本論文使用 OpenMP 架構，並利用簡易的區域分割以平行化程式，更進一步地加速求解。在物理問題方面，本論文採用拉穴流、自然對流以及雙擴散浮力引導流，以進行數值方法以及程式整體的驗證，同時比較使用多重網格法以及傳統迭代法的運算時間差別。
在開放水閘所引致的異重流問題中，本論文比較在層流與紊流的條件下，探討 Kelvin-Helmholtz instability 以及 Lobe and cleft 不穩定性 (instability) 的模擬結果，另外，本論文也比較了在二維水槽以及兩種不同寬度的三維水槽問題中，其寬度對於流場的影響以及邊界所造成的渦度變化。

關鍵字

多重網格法 ； Neumann 邊界 ； Poisson 方程 ； 異重流 ； Kelvin-Helmholtz instability ； Lobe and cleft instability

並列摘要

In this thesis, multigrid method is used to improve the computational efficiency of solving the pressure Poisson equation. The multigrid method with arbitrary level under two different grid systems is implemented, and the comparison of computational efficiency between V-cycle and Full-cycle is also made. In addition, OpenMP architecture and a simple domain decomposition are used to parallelize the program so as to accelerate the computation. The models of lid-driven cavity, the natural convection in a cavity and the double-diffusive convection in a cavity are adopted to verify the numerical method and compare the execution time between the multigrid method and the traditional iterative method.
In the lock-exchange gravity current problem, this thesis investigates the Kelvin-Helmholtz instability and the lobe-and-cleft instability under laminar and turbulent conditions. In addition, the wall effect and the vorticity are also compared in the two-dimensional and three-dimensional problems with different channel widths.

並列關鍵字

Multigrid method ； Neumann B.C. ； Pressure Poisson equation ； Lock-exchange gravity current ； Kelvin-Helmholtz instability ； Lobe and cleft instability

參考文獻

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