ABSTRACT: Presented is a numerical method for simulating free-surface flows through solution of the time-dependent, incompressible, Navier-Stokes equations and the non-linear dynamic and kinematic boundary conditions. The numerical method uses boundary-fitted curvilinear coordinates with a finite-volume, time-splitting, approximate-factorization method formulated in primitive variables on a non-staggered grid. The pressure Poisson equation is solved using a multigrid technique. A new extension of domain decomposition methods is developed which involves splitting the free surface from the fluid volume for the iterative enforcement of the pressure equation and the dynamic boundary condition. A derivation in curvilinear coordinates of the Eulerian kinematic boundary condition is presented and is used for advancing the free surface in a Crank-Nicolson formulation. Development of the numerical method is presented for three dimensions; preliminary results are given from two-dimensional non-linear simulations of standing waves.

EXTRACT: Figures 1 and 2.

Figure 1: (left) Restricted curvilinear coordinate grid. Figure 2: (right) Generalized curvilinear coordinate grid

ACKNOWLEDGMENTS: Supported the Fluid Dynamic Program, Office of Naval Research under grant nos. N00014-91-J-1200 and N00014-94-J-0190.