Numerical Simulations of Laminar Free-Surface Flows

Numecrical simulations are presented for two-dimensional laminar flows of a Newtonian fluid past a square obstacle placed in a steady stream close to a free surface. The viscous, incompressible Navier-Stokes equation. supplemented by approximate dynamic and kinematic boundary conditions at the free surface, are solved, so that the water surface elevaion can he integrated into the solution and solved for, togheter with the velocity and pressure fields. An immersed boundaries technique has been used to take in account the presence of a solid body in the fluid stream: High resolution is achieved in the near-wall regions by utilizing a variable or clustered grid in physical space, with an increasing density of computational point near the boundaries. The flow pattern, vorticity contours and pressure contours are presented for steady and unsteady rcgimes at low Reynolds numbers over a range of Froude numbers. Results are analyzed in terms of vorticity generation and interaction, and flow-induced forces on the body.