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題 名 | Discontinuous Finite Element Method for Two Dimensional Conservation Laws=不連續有限元素法解保守場問題 |
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作 者 | 施昇昌; 林三益; | 書刊名 | 中國機械工程學刊 |
卷 期 | 20:2 1999.04[民88.04] |
頁 次 | 頁121-127 |
分類號 | 447.55 |
關鍵詞 | 不連續有限元素法; 二維保守場; Aeroacoustics; Finite element method; Limiter; Maximum principle; |
語 文 | 英文(English) |
中文摘要 | 本文發展和分析一個高階有限元素法計算二維保守場問題。本數值法適用於計算 聲學問題。此方法採用不連續的有限元素法,在每個格點建立六個基本元素,利用積分法則 求得六個時間的常微分方程系統,再用時間積分法求得六個量。此六個量分別代表物理變數 的平均值,x和y方向的二個一次微分值和三個二次微分值。並引進適當的限制函數使得此 數值法滿足極大值原理。原則上,此方法為空間三階準確度和時間二階準確度。一系列的數 值結果顯示此方法的準確性和適用性。 |
英文摘要 | A finite-element method has been developed and analyzed (or solving two dimensional conservation laws on rectangular meshes. Specially, the method is applied to the computational aeroacoustics. The method is based on a discontinuous Galerkin finite-element method in the space discretization, and a three-stage TVD (Total Variation Diminishing) Runge-Kutta method in the time marching. In this paper, we construct six independent bases on each grid element and a local limiter to ensure that the scheme satisfies the maximum principle. The method is formally third-order accurate in space and second-order accurate in time. Preliminary numerical results on scalar and system initial-boundary value problems are shown to demonstrate abilities of the numerical method. |
本系統中英文摘要資訊取自各篇刊載內容。