Numerical Solution to the Free Liquid Surface under Gravity
Hou Wen,Ma Tiehua,Liu Shuangfeng
(Key Lab for Instrumentation Science and Dynamic Measurement North China Institu te of Technology, Ministry of Education, Taiyuan 030051, China)

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. As pecified coordinate transformation is adopted to avoid the over-stiffness in numerical evaluation. Some numerical examples are provided.
Keywords: surface tension，curvature，differential equation，accelerometer，hydrostatics.