Free surface flow with an oscillating cylinder based on a viscous
incompressible two-fluid model
An accurate computational method for a viscous incompressible fluid flow past a
circular cylinder beneath the free surface is presented. The method is
designed for studying free surface problems with arbitrary moving circular
cylinders. The method of solution is based on a finite volume discretization of
the two-dimensional continuity and unsteady Navier-Stokes equations in their
pressure-velocity formulation on a fixed Cartesian grid. Well-posed boundary
conditions are enforced at the inflow and outflow boundaries since they ensure
correct physical development of the flow near the computational domain
boundaries. The free surface boundary conditions are applied implicitly by
using a two-phase flow technique which treats the air phase and the fluid phase
as a single fluid with variable material properties. The displacement of a free
surface is tracked by using the volume of fluid method. The fractional
area/volume obstacle representation method is combined with the cut cell method
to improve the accuracy of the spatial discretization of a fluid-body
interface. The numerical algorithm is verified by applying it to the special
case of uniform flow past a cylinder undergoing forced oscillations in
streamwise direction in the presence of a free surface.
The author acknowledges the significant intellectual contributions of both O.
I. Gubanov and L. A. Mironova to this paper which is derived from their M.Sc.
and Ph.D. works, respectively.