| A Crank-Nicolson finite difference method for linearized Navier-Stokes equations is developed to simulate the numerical solution.A coordinate transformation is applied to map the irregular fluid domain onto a square domain.Furthermore,the mathematical model is solved in a square fixed staggered mesh system.Finally,the iterative algorithm is adopted to solve Navier-Stokes equations.The free surface elevations and vortexes of the flow field are numerically simulated.The main results 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 linearized Navier-Stokes equa-tions.The free surface elevations have been numerically simulated under free oscil-lation and pitching oscillations.It is found that the free surface wave oscillates with decaying amplitude in the viscous fluid domain,and as the Reynolds numbers and dissipative parameters increases,the free surface elevation decays slower.Under the short-period pitching excitation,clear single vortex period is seen when the tank is excited by pitch motion with different Reynolds numbers,dissipative parameters and pitching motion frequency.(2)Based on the numerical solution of the linearized Navier-Stokes equations,a Crank-Nicolson finite difference method based on the coordinate transformations is used to study the numerical solution of the Navier-Stokes equations.The vortexes are studied under forced pitching oscillation and coupled vertical and pitching oscillations.It is found that the single vortex has changed to double vortex in case of a long-period pitching excitation,and the single vortex appears longer at high Reynolds number and dissipation parameters.The free surface wave oscillates with decaying amplitude in the viscous fluid domain under coupled vertical and pitching oscillations.And the double vortex appears only at large amplitude of pitching excitation. |
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