非線性自由液面不可壓縮黏性流場之數值模擬

Numerical Simulation for Fully-Nonlinear Free-Surface Viscous Flow of Incompressible Fluid

洪立萍(Li-Ping Hung) ； 蔡武廷(Wu-Ting Tsai)

《中國航空太空學會學刊》 36卷4期 (2004/12) Pp. 349-358

https://doi.org/10.6124/TAASRC.200412_36(4).04

摘要

本研究旨在建立一非線性自由液面、三維不可壓縮黏性流場之數值模式，以進行未來之自由液面紊流模擬。爲滿足非線性自由液面邊界條件，我們利用座標轉換將隨時間變動之物理邊界與流場控制方程式映射至規則的計算區域，分別以偽頻譜法與二階有限差分法近似轉換方程式中之水平與垂直微分項，並以低儲存量之二階Runge-Kutta法進行時間積分。爲滿足不可壓縮流的條件，壓力場需滿足一Poisson方程式，此經座標轉換之Poisson方程式爲不可分離的方程式，故需以疊代法求解，並應用牛頓法加速疊代的收斂。二維非線性黏性駐波與前進波的計算結果驗證了此模式之準確性與可用性。

關鍵字

非線性自由液面流 ； 三維黏性流場 ； 不可壓縮流 ； Poisson方程式 ； 數值模擬 ； 牛頓疊代法

並列摘要

We develop a numerical model for simulating three-dimensional, fully-nonlinear free-surface flow of viscous, incompressible fluid. The nonlinear free-surface boundary conditions are satisfied on the moving boundary exactly. Coordinate transformation is used to map the physical domain to a regular computational domain where the momentum equations are integrated in time and the solenoidal condition is satisfied by solving the transformed pressure Poisson equation. Pseudo-spectral and finite-difference methods are used to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. Low-storage, second-order Runge-Kutta scheme is employed for time integration. A modified Newton's method is used to accelerate the iterative solution of the non-separable pressure Poisson equation. The accuracy and efficiency of the numerical model is demonstrated by simulating the evolutions of nonlinear standing waves and nonlinear progressive waves of viscous fluids.

並列關鍵字

Fully nonlinear free-surface flow ； Three-dimensional viscous flow ； Incompressible fluid ； Poisson equation ； Numerical simulation ； Modified Newton's iteration method