臺灣博碩士論文加值系統

在本研究中，我們利用微分容積法求解規則區間之熱傳問題，探討其在
數值模擬的準確性與適用性，並藉由格點產生法與有限元素法中主要元素
的概念，配合區間分割的技巧，將其推廣至不規則區間求解。從研究結果
顯示，微分容積法之某一特定點性質與區間內所有格點有關，其數值模擬
結果會比有限差分法或是微分成方法在相近格點數下，求解所得誤差較小
。此外，利用微分容積法求解熱傳問題上，無論在三角形區間、矩形區間
、不規則區間、或是將區間分割都可模擬出不錯的結果。

The applicability and accuracy of differential cubature method
(DCM) are investigated by solving several heat transfer problems
in rectangular domain. In addition, problems in irregular
domains are also analyzed by DCM in conjunction with the
concepts of domain decomposition as well as master elements
adapted from the finite element method. It is found that good
results can usually be obtained by DCM. In addition, the
accuracy of DCM can strongly influenced by the distribution of
the grid points (nodes) . However, under similar grid-point
distribution, small L2norm errors can usually be achieved by DCM
than those obtained by finite difference method (FDM) and
differential quadrature method (DQM). Investigations on the
determination of optimum grid-point distribution in DCM shall be
conducted in further studies.