Oscillation of a floating body in a viscous fluid

Abstract

The nonlinear viscous-flow problem associated with the heaving motion of a two-dimensional floating cylinder is considered. It is formulated as an initial-boundary-value problem in primitive variables and solved using a finite-difference method based on boundary-fitted coordinates. A fractional-step procedure is used to advance the solution in time. As a case study, results are obtained for a rectangular cylinder oscillating at a Reynolds number of 103 . The nonlinear viscous forces are compared with those of linear potential theory. An assessment on the importance of viscous and nonlinear effects is made. The solution technique is sufficiently robust that extensions to consider other single and coupled modes of motion are possible.

An Improved Mac Method (Simac) for Unsteady High-Reynolds Free Surface Flows

“…10,11 Despite the great accuracy of these methods, they require a large amount of CPU time and their effectiveness in handling highly distorted free surface patterns has yet to be proved.…”

“…Later on Esposito 15 proved that a consistent scheme can be achieved by explicitly introducing the physical pressure in equation (8) (10). In this scheme the physical pressure is related to the operator F by the equation…”

A new method for simulating rigid body motion in incompressible two‐phase flow

“…Results are shown in comparison to those from [28,29] in Figure 11 for a grid size of x = y = 0.3 m. In both the current and previous numerical studies the heave motion of the cylinder decays over a 10-s simulation period and the center of mass settles to the predicted position (indicated by the dotted line) based on buoyancy. The Reynolds number in this case can be defined [30] by…”

Viscous and inviscid matching of three-dimensional free-surface flows utilizing shell functions

“…The evaluation of the integrals in the Green-function coefficients (17)(18)(19)(20) (which appear in the matrices (23-26)), and the convolution of the past solution with the Green-function coefficients (summations in E p , Eq. 27).…”

“…To complete each step, a pressure field is then found that corrects the intermediate velocity field to form the velocity and pressure field at the new time-step. This is a method that falls into the class of projection methods proposed by Chorin [17] and developed for use with free-surface flows by Yeung [18] in two dimensions and by Yu [16,19] in three dimensions. A time-difference scheme between the old (K − 1) and new (K ) time-steps provides,…”