TY - JOUR
T1 - Modified Verlet Method Involving Second-Order Mid-Point Rule Applied to Balls Falling in One-Dimensional Potentials
AU - Hidenori Yasuda
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 1
EP - 19
PY - 2018
DA - 2018/02
SN - 1
DO - http://doi.org/10.4208/eajam.160909.310310a
UR - https://global-sci.org/intro/article_detail/eajam/10893.html
KW - Verlet method, falling balls, first return map, phase separation, shallow water equations.
AB - <p style="text-align: justify;">A modified Verlet method which involves a kind of mid-point rule is constructed
and applied to the one-dimensional motion of elastic balls of finite size, falling
under constant gravity in space and then under the chemical potential in the interface
region of phase separation within a two-liquid film. When applied to the simulation
of two balls falling under constant gravity in space, the new method is found to be
computationally superior to the usual Verlet method and to Runge–Kutta methods, as it
allows a larger time step for comparable accuracy. The main purpose of this paper is to
develop an efficient numerical method to simulate balls in the interface region of phase
separation within the two-liquid film, where the ball motion is coupled with two-phase
flow. The two-phase flow in the film is described via shallow water equations, using
an invariant finite difference scheme that accurately resolves the interface region. A
larger time step in computing the ball motion, more comparable with the time step in
computing the two-phase flow, is a significant advantage. The computational efficiency
of the new method in the coupled problem is demonstrated for the case of four elastic
balls in the two-liquid film.</p>