含渦流作用之重力水波研究(2/2)

Abstract

In this study, a grid-free numerical model for the simulation of gravita- tional water wave with vortex effect is proposed. The computational algo- rithm is established by combining a potential flow field with a vortex flow field. The potential at the free surface and the free-surface displacement are solved by the time integrations. The vorticity field is the solution of the vor- ticity equation, which is solved using the vortex method and the vortex sheet method. The potential and velocity fields are solved by the boundary integral method. Two cases are applied to validate the proposed model, and the vortic- ity shedding due to the rectangular obstacle in the linear wave is simulated. These results show the ability of the proposed model for the simulations of free-surface flows with vortex effect.

本計畫採用勢流、渦流結合計算的方式，建立一不需於計算域內建構網格，而能計算渦流影響之重力水波數值模式。本研究採用Helmholtz Decomposion ，將速度場分為irrotational part 與rotationalpart 兩部分，再分別以勢流場及渦流場之適當數值方法求解。但是對於具有自由邊界待解之問題─如同本研究探討之水波問題，則因需求解自由水面之運動與動力邊界條件，因此問題將顯得較為複雜。本研究之目的，即為解決自由邊界條件的勢流場/渦流場合併計算的數值模式。 本研究應用兩個計算例測試模式的正確性，並計算受線性水波影響下的矩形物體產生的渦流現象。由這些計算例可以顯示本模式可以有效地模擬受渦流影響的二維線性水波問題。