以平行化直接模擬蒙地卡羅法模擬自由分子流到近連續流的空穴超音速流場

Abstract

空穴流場是很基本的流體力學問題，在過去也有很多人做過相關的研究。但是大多數人都是討論連續及不可壓縮流的流場，較少數人針對近連續流到稀薄流體區的流場作研究。因此我們對此做一有系統的探討 本文描述使用直接模擬蒙地卡羅法來模擬從稀薄流體區到接近連續流體範圍的二維上板空穴流場。為了確保能在較鄰近的分子發生碰撞，運用transient sub-cells [Tesng, et al., 2007] 的功能，使得同時降低計算負荷及記憶體使用量。比較使用transient sub-cells功能和不使用transient sub-cells功能之模擬結果來驗證正確性。驗證結果顯示出使用transient sub-cells功能可以使用大約平均自由路徑大小的網格且擁有正確性，並且大量減少計算負荷，特別是在接近連續流體範圍。流動結構被詳細討論包含上板驅動速度由馬赫數1.1到4和Kn數(與平均自由路徑和cavity大小有關)由10到0.0033。 由結果顯示出速度滑動現象會在Kn 的影響中表現的較M的影響為明顯。在Kn=0.01 和 0.0033 的模擬結果, 都有再右下角出現第二渦流；且Kn=0.0033 在M=4的情況下會在左下角也出現第三渦流。固定Kn=0.01與0.0033，當馬赫數升高時渦流中心點會往左下方移動；但是當固定於高Kn，隨著馬赫數增加渦流中心卻往相反方向移動。

The driven cavity flow is one of the fundamental fluid flow problems with simple geometry that was often used as the benchmark test problem in computational fluid dynamics. Although they have been thoroughly studied in the literature, most of them were focused on incompressible or continuum compressible regime. Very few have been done in the rarefied and near continuum regimes. It may serve as the benchmarking problem for extending numerical scheme into flow in these regimes. Thus, this thesis describes the simulation of a two-dimensional supersonic driven cavity flow from free-molecular to near-continuum regime by directly solving the Boltzmann equation using the parallel direct simulation Monte Carlo method. Transient sub-cells [Tesng, et al., 2007] were implemented on a general unstructured grid to meet the nearest-neighbor collision requirement, while keeping minimal computational overhead and memory requirement simultaneously. Accuracy of simulation of transient sub-cells using larger sampling cell size was verified by comparing the results with that using much finer sampling cell size. Results show that transient sub-cells can greatly reduce the computational cost, which is especially important in the near-continuum regime. Flow structures within a driven cavity flow are then discussed in detail by varying the top plate speed (Ma=1.1-4) and Knudsen number of cavity (Kn=10-0.0033), in which the corresponding Reynolds number is in the range of 0.181- 1997.6. Results show that velocity slips and temperature jumps along the solid walls increase with increasing Knudsen number at the same Mach number. The additional second vortex occur at the right bottom wall in all Kn=0.01 and 0.0033 case. The Kn=0.0033 and M=4 has the third vortex at the left bottom corner. Results show that vortex center move toward left and down as Mach number increasing at the same Kn=0.01 and 0.0033. But the vortex center move toward the opposite way for Kn=10, 1 and 0.1.