【摘要】 给出一种重力作用下静止液体自由面的数值解方法。根据流体力学Young-Laplace公式和微分几何学主曲率方程,并利用液体自由面的对称性质,导出重力作用下静止液体自由面母线的常微分控制方程。为了使该方程便于利用现有的Runge-Kutta法,根据问题的物理背景,将体积边界条件转化为固-液接触面半径条件;采用一种坐标变换,避免了该方程数值计算中刚性问题的出现。最后给出了算例。更多还原

【Abstract】 The differential equation governing the curvature of free surface of static liquid is deduced based on the Young-Laplace formula,the principal curvature function and the symmetry of the surface configuration simultaneously are employed.To take advantage of Runge-Kutta method,a conversion of the volume condition into radius condition of liquid-solid interface is carried out.A specified coordinate transformation is adopted to avoid the overstiffness in numerical evaluation.Some numerical examples are provided.更多还原