Numerical Simulation for Fully-Nonlinear Free-Surface Viscous Flow of Incompressible Fluid

摘要

We develop a numerical model for simulating three-dimensional, fully-nonlinear free-surface flow of viscous, incompressible fluid. The nonlinear free-surface boundary conditions are satisfied on the moving boundary exactly. Coordinate transformation is used to map the physical domain to a regular computational domain where the momentum equations are integrated in time and the solenoidal condition is satisfied by solving the transformed pressure Poisson equation. Pseudo-spectral and finite-difference methods are used to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. Low-storage, second-order Runge-Kutta scheme is employed for time integration. A modified Newton's method is used to accelerate the iterative solution of the non-separable pressure Poisson equation. The accuracy and efficiency of the numerical model is demonstrated by simulating the evolutions of nonlinear standing waves and nonlinear progressive waves of viscous fluids.