摘要
研究了在二维水槽带非线性自由面边界条件的Navier-Stokes方程的数值解.通过σ坐标变换对不规则的水槽液体区域变换为一个规则的正方形区域,运用交错网格技术,采用较为稳定的Crank-Nicolson格式,建立流场变量的耦合迭代的算法,求解了粘性不可压缩的Navier-Stokes方程的数值解.数值模拟了水平激励和垂直激励下的自由面波高的值.数值结果表明,与无粘的Euler方程的数值解比较,粘性效果造成的自由面波的衰减非常明显.
A numerical solution algorithm of Navier-Stokes equation with nonlinear free Surface boundary condition is developed. A finite difference method is developed and is applied to solve Navier-Stokes equation in a two dimensional tank. A staggered mesh system is employed and a a coordinate transformation is applied. A Crank-Nicolson scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition. The Crank-Nicolson method is an unconditionally stable and implicit numerical scheme with second-order accuracy in both time and space. In the final, the numerical solutions are presented and agree well with the analytic solution and previously published results.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2012年第2期55-61,共7页
Acta Scientiarum Naturalium Universitatis Nankaiensis
