以變動座標描述次層流理論模型之應用

根據水土保持手冊所定義，土石流乃為泥、砂、礫石等物質與水之混合體，在地質與地形條件影響之下，受重力作用及內部應力分布的轉變後所產生之流動體，流動於複雜的地形上。本篇論文將會延伸對於Fraccarollo & Capart [2002] 的概念中，結合了通用座標系統（Unified coordinate System）之特性，建立一新的任意地型上包含侵蝕與堆積現象的次層流模型（Sub-layer model）。其上層是水，中間為水與固體砂石之混合流體，最下層為砂石所構成之底床。在次層流的流動過程中，將會有不斷的侵蝕與堆積現象在底床與混合流體間發生，在Fracarrolo & Capart [2002] 篇中，將此現象在於卡式座標中描述；在本篇論文中，將試著將此結果轉換至變動座標當中。隨著時間與底床的侵蝕堆積情形，底床隨著時間位置而不斷在改變，將變動座標之軸緊貼著此變動底床，則是垂直於底床方向，本篇將試著在此座標下，透過深度積分得出質量、動量守恆與底床侵蝕率之形式。再來本研究利用non-oscillation central （NOC）有限體積差分法，試著將此理論模型作一模擬。由於理論模型採用通用座標統達成座標隨著底床變動的特性，我們得以模擬探討水體潰壩的過程中，底床受到侵蝕堆積之情形。

關鍵字

通用座標系統

並列摘要

According to the manual definition of conversation of water and soil, Landslides is the mixtures of such materials as mud, sand and water. Under the gravitational form and redistribution of internal stress states. Due to change of geological and topological coordinate, the materials are transported over complex topography. We aim to extends the concept of Fracarrolo & Capart[2002] and combine the characteristic of Unified Coordinate System to establish a new Sub-layer model on general topography including corrosion and accumulation in this thesis. Its upper layer is water, the middle is mixed fluid of water and solid grit, and the bottom bed is formed by grit. In the course of flow of sub-layer flow there will be unceasing phenomena of corrosion and accumulation on the bottom bed and mixed fluid flow these phenomena are taken into account in a Cartesian Coordinates System in Fracarrolo & Capart [2002]. We try to reformulate the result into variable coordinates. The coordinate are chosen to coincide with the bottom bed, and they change along with the time due to corrosion and accumulation. The in variable coordinates sticks on the variable bottom bed, and is normal to the direction of the bottom bed. A set of depth integrated mass and momentum conservation laws are derived. To investigate the key feature of this model we applied the non-oscillation central (NOC) finite volume scheme with respect to a dam-brake problem. The evolution of the corrosive/accumulative based surface is obtained, which were quantitatively compared with respect to different density ratio s, volume fraction as well as the thickness of the mixture layer .

並列關鍵字

Unified Coordinate System

參考文獻

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