結論

本研究為了解決開放性邊界的問題，以吸收性邊界配合修正 LODI 法，以混 合式邊界條件完成在正方形平行平板間自然對流的計算。本研究成功整合了低速 可壓縮流的數值計算方法與開放性邊界條件的應用，發展了幾乎完整涵蓋所有流 體問題的計算方法。本研究的主要貢獻如下：

1. 低速可壓縮流的計算方法：

過去的多利用流體速度將其區分為可壓縮與不可壓縮流，此種方法限制許多 實際的應用，如高溫自然對流、引擎內部流場與聲場的計算等。本研究利用正方 形 平 行 平 板 自 然 對 流 驗 證 計 算 方 法 的 適 用 性 ， 且 由 於 溫 差 極 大 ， 不 使 用 Boussinesq 假設來完整計算出浮力效應對流體的影響。

2. GPU 高速平行運算：

由於本研究需要大量的計算資源，為了提升效率節省計算時間與資源，利用 GPU 高速平行運算技術取代傳統的 MPI 與 OpenMP 方法，達成使用個人電腦計 算複雜問題的目的。

3. 開放性邊界條件之應用：

本研究以吸收性邊界條件配合修正 LODI 法，成功解決在開放性邊界上，邊 緣與角落造成的數值不穩定現象，並提高吸收性邊界的效率，以之計算出正方形 平行平板間自然對流的現象，並探討不同加熱位置熱傳機制的差異。此外，對於 高雷利數下之自然對流由層流轉變為紊流的不穩定現象也完整的呈現。

綜上所述，本研究所發展之邊界條件與數值方法將可作為各種開放性邊界問 題之基礎並可進而精準解出各種複雜的流體問題。

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