http://scholars.ntou.edu.tw/handle/123456789/14677
標題: | Fractional step-method of characteristics for solving shallow-water type equations | 作者: | 蔡加正(Chia-Cheng Tsai) 莫漢默德(M. Enamul Quadir) 許泰文 |
關鍵字: | 分布特性線法;類淺水波方程式;底床摩擦力;fractional step-method;method of characteristics;shallow-water type equations;bottom friction | 公開日期: | 1-十二月-2011 | 出版社: | 台灣海洋工程學會 & Ainosco Press | 卷: | 11 | 期: | 2 | 起(迄)頁: | P119 - 135 | 來源出版物: | Journal of coastal and ocean engineering | 摘要: | 本文回顧如何以分布特性線法解類淺水波方程式,我們考慮淺水波在含摩擦力之任意形狀底床上之運動,分布法能夠把二維以上多變數耦合的類淺水波偏微分方程式,轉為數條一維的偏微分或常微分方程式,在解題的過程中,對流階段以特性線法處理,而非對流階段則以龍閣庫塔法或解析解法處理。其中特性線法的部分,我們把數條一維的耦合偏微分方程式轉為黎曼不變量的非耦合常微分方程式,而特性線與格點交錯的部分,則以內差法處理。本方法在一些類淺水波方程式的可應用性,則以數值結果與其他文獻上的實例來強化。This article gives a review of the formulation of fractional step-method of characteristics (FSMoC) for solving shallow-water type equations. The formulation is demonstrated by a shallow-water type equation with sources of force, arbitrary bottom topography and friction force. The fractional step-method (FS) splits the multidimensional shallow-water type equations into sequential augmented one-dimensional problems (PDEs or ODEs). Among the sequential problems, the advection phases are solved by the method of characteristics (MoC) and the non-advection phases are solved either by analytical methods or the Runge-Kutta method. In MoC, the one-dimensional PDEs are transformed to ordinary differential equations using Riemann invariants, which should be interpolated at each time step since the characteristic curves do not fall on a grid system. The applicability of the prescribed formulation is demonstrated by numerical results or strengthened by the studies in literature. |
URI: | http://scholars.ntou.edu.tw/handle/123456789/14677 | DOI: | 10.6266/JCOE.2011.1102.03 |
顯示於: | 河海工程學系 |
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