臺灣大學: 土木工程學研究所楊德良王子禎Wang, Tzu-ChengTzu-ChengWang2013-04-012018-07-092013-04-012018-07-092010http://ntur.lib.ntu.edu.tw//handle/246246/255718中文摘要 本研究提出一個改良的區域化已積分之徑向基底函數微分積分數值方法(localiRBF-DQ method)，以求解高哈特曼數之穩態磁性流體動力管流。此處提出的區域化已積分之徑向基底函數微分積分數值方法是利用所求點的附近點之線性加權函數值之總和來離散化所求點之微分值，是一個真正不需要建立網格且在計算上非常有效率的數值方法。而所使用的已積分之徑向基底函數可以比傳統的徑向基底函數在模擬求解控制方程式之近似解時，更加的穩定。在高哈特曼數(Hartmann numbers)(高磁場)的情況下，磁性流體動力(MHD)的問題被廣泛的應用在熱核融合反應爐的包層裡液態金屬冷卻系統的設計上。本研究會提供在完全絕緣以及部分絕緣且部分傳導的邊界條件和哈特曼數到達10 5的情況下，矩形、圓形甚至任意形狀斷面的數值解。藉由這些數值結果證實，在哈特曼數小於等於10 5的範圍內，此篇論文所提出的方法都有能力去得到精確且穩定的速度和感應磁場之近似數值解。Abstract In this paper, a localized integrated radial basis function-based differential quadrature (iRBF-DQ) method for solving steady magnetohydrodynamic (MHD) duct flow is presented. Local iRBF-DQ method is a truly meshless and computationally efficient method, which discretizes any derivative at a knot by weighted linear sum of functional values at its nearby nodes. The integrated RBFs make the approximations of governing equations more stable than conventional RBFs. The high Hartmann numbers (high magnetic field) MHD problem apply to the design of cooling systems with liquid metals for a thermal nuclear fusion blanket. We present results for Hartmann number up to 10 5 with fully insulating or partly insulating and partly conducting walls, having rectangular, circular and arbitrary cross section. The evidence shows that local iRBF-DQ method has the ability to produce accurate and stable approximations for the velocity and induced magnetic field at the range of Hartmann number≤10 5.4665130 bytesapplication/pdfen-US已積分之徑向基底函?配置法區域化已積分之徑向基底函?微分積分?值方法薄板樣條函?無網格磁?體動?學馬克士威方程組那維爾史托克方程組哈特曼?哈特曼效應自?式液態?屬包層integrated radial basis function-based (iRBF) collocation methodlocalized integrated radial basis function-based differential quadrature (iRBF-DQ) methodThin Plate Splines (TPS)meshlessmagnetohydrodynamic (MHD)Navier-Stokes equationsHartmann numberHartmann effectself-cooled liquid metal blanketsthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/255718/1/ntu-99-R97521320-1.pdf