Numerical Simulation Study Of The Hydrodynamics Of Two-dimensional Incompressible Navier-Stokes Equations

The numerical solutions of the Navier-Stokes equations and the Navier-Stokes e-quations with dissipative term in two-dimensional rectangular tanks are studied in this paper. The free surface elevations and vortexes within the flow field are numerical-ly simulated. Firstly, the mathematical models based on the Navier-Stokes equations and the Navier-Stokes equations with dissipative term are built, respectively. Then, the irregular physical domain is mapped onto a fixed square computational domain by the coordinate transformation and a staggered mesh system is employed in the com-putational domain. Finally, the Crank-Nicolson finite difference method and iterative algorithm are adopted to solve the two different mathematical models. The main works of this paper are as follows:(1) A Crank-Nicolson finite difference method based on the coordinate transfor-mations is used to study the numerical solution of the Navier-Stokes equations. The free surface elevations have been numerically simulated under free oscillation, forced horizontal oscillation, forced vertical oscillation, forced pitching oscillation, coupled horizontal and pitching oscillations and coupled vertical and pitching oscillations. The variations and periods of the vortexes have also been studied in detail under forced pitching oscillation, coupled horizontal and pitching oscillations and coupled vertical and pitching oscillations. Furthermore, the numerical results are also compared with the linearized analytical solutions and other reported numerical data to verify the valid-ity of the present numerical method.(2) A Crank-Nicolson finite difference method based on the coordinate transfor-mations is used to to study the numerical solution of the Navier-Stokes equations with dissipative term. The free surface elevations with different dissipative parameters have been numerically simulated under free oscillation, forced horizontal oscillation, forced vertical oscillation, forced pitching oscillation, coupled horizontal and pitching oscil-lations and coupled vertical and pitching oscillations. The effects of dissipation on the variations and periods of the vortexes have also been analyzed in detail under forced pitching oscillation, coupled horizontal and pitching oscillations and coupled vertical and pitching oscillations.