Accurate computation of free surface flow with an oscillating circular cylinder based on a viscous incompressible two-fluid model

This thesis focuses on the design of a new computational model for a class of free surface flows with a moving circular cylinder based on a viscous incompressible two-fluid model. 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. The displacement of the free surface is tracked by using the volume of fluid method. The positions of both the free surface and fluid-body interfaces are determined at each time step by using the piecewise linear interface calculation algorithm. The advection of the reconstructed free surface with local velocity field is performed by the geometrical area preserving volume of fluid advection algorithm. 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. Discrete pressure and velocity fields corresponding to the successive time instants are obtained as a result of solution of a coupled sparse linear system in primitive variables using a generalized minimal residual method. This is done by making use of the Trilinos numerical solver library. The accuracy checks indicate that the resulting method is of second-order in space and first-order in time. -- The numerical algorithm is applied to the problem of unsteady, laminar, two-dimensional flow of a viscous incompressible fluid past a circular cylinder undergoing forced oscillations in streamwise direction in the presence of the free surface. This is the first numerical study conducted on this problem to date. The validation of the method is presented in special cases and good comparisons with previous experimental and numerical results are obtained