Numerical Simulations of Breaking Free-Surface Flows

本論文的主旨在於建立一套系統性的數值模式來模擬自由液面流中含碎波現象之問題。欲處理此複雜的流體動力問題，數值的運算通常包括二個要件: 一、可靠而有效率的運算核心 。二、精確的自由液面捕捉方式。首先，在運算核心部份，我們分別嘗試運算子拆解法與SOLA數值技術求解原始變數型態的奈維爾-史托克斯方程式。再者，數值上常見的自由液面的捕捉方式分別為表面追蹤法以及表面捕捉法，二者皆於文中個別做探討。本文主要提出二種處理方式來模擬自由液面的變化，分別使用修正型的高度函數法以及改良型的流體體積法計算之，其主要區別在於描述液面含有碎波現象與否。上述二方法的共通點皆基於滿足質量或體積守恆的條件下做流體動力的分析。此外，於數值驗證中若物理條件包含水中結構物，則採用結合卡氏沈浸邊界法的結構性網格描述其運動行為。最後，擬將以上所提出的要件做結合即可處理自由液面流中含有碎波現象的問題。文中所有數值計算的結果和文獻資料比較都相當吻合，以證明此數值模式開發的可行性。The thesis is concerned with developing a numerical model to study the breaking free-surface flow problem. However, such a robust numerical model in computational fluid dynamics must be composed of the reliable flow solver and the accurate prediction of variations of free surface. At first, the mathematical model is based on solving the Navier-Stokes equations with the operator splitting procedure by a two-step projection method or a solution algorithm with successive over relaxation scheme. Second, to capture the configurations of free surface, the interface tracking and the interface capturing treatments are both concerned in this thesis. Two accurate methods, including the modified height function method and the advanced volume of fluid method, are respectively proposed. The difference between the two proposed methods depends on the access of describing the breaking effects or not. The common mission of the two methods is to benefit the rule of mass/volume conservation in computations. However, to describe the motions of obstacle embedded in the fluid, capability of handling the complex geometry is relied on the hybrid Cartesian immersed boundary method. Finally, the links of flow-field solutions and proposed schemes are used to study the free-surface flow problem with liquid-breaking effects. All the numerical results in this thesis are compared favorably with the reference data. Reasonably good agreements can be observed through the developed numerical model