摘要 本研究主要利用分散式平行運算系統,對最小平方有限元素法(LSFEM) 進行平行化應用在二維及三維的數值流場進行模擬。首先使用區域分割法(Domain Decomposition) 之方式在元素(Element)上進行平行,並且討論以不同的網格數及節點數,在不同數目的CPU 上進行處理。比較循序化(Sequential Code) 與平行化(Parallel Code)在計算結果之誤差百分比、流場現象與平行效益(Parallel Efficiency)之情形,模擬結果雖因網格密度、時間間隔、精確度等會造成些許的誤差,但整體結果發現平行化所得之結果與原來循序化結果相符合,使用不同數量的CPU 可以明顯的縮短50%~100% 效果,因此可以預估在未來以LSFEM 進行複雜的數值計算時,分散式平行運算必可以加入LSFEM 模式中作為高效率的計算工具。
ABSTRACT This thesis utilizes the distributed memory multi-processors system to find the solution of two-dimensional and three-dimensional flow fields with the modified least-squares finite element method. Use the way of domain decomposition to parallel on element with different numbers of CPU, and to study the effect on computation with different grids and nodes. The parallel code is compared with the sequential code in the error percentage of the calculated results, flow fields and parallel efficiency.Although there is minor discrepancy due to the mesh density, time step size and accuracy, the comparison of simulated results between the parallel code and sequential code shows good agreement. The CPU time for parallel code is shortened obviously by about 50% to 100% for using CPU up to 8 different processes. The application of parallel computation on complicated problems in computational fluid dynamics with LSFEM in the future will be a high-efficiency computational tool.