A meshless collocation method based on radial basis functions is proposed for solving the steady incompressible Navier–Stokes equations. This method has the capability of solving the governing equations using scattered nodes in the domain. We use the streamfunction formulation, and a trust-region method for solving the nonlinear problem. The no-slip boundary conditions are satisfied using a ghost node strategy. The efficiency of this method is demonstrated by solving three model problems: the driven cavity flows in square and rectangular domains and flow over a backward-facing step. The results obtained are in good agreement with benchmark solutions.

With the increase of ship size, the stiffness of the hull structure becomes smaller. This means that the frequency of wave excitation tends to be closer to the natural frequency of the hull vibration, which in turn makes the hydroelastic responses more significant. An accurate assessment of the wave loads and motion responses of hulls is the key to ship design and safety assessment. In this paper, the coupled CFD (Computational Fluid Dynamics)-FEM (Finite Element Method) method is used to investigate the non-linear hydroelasticity effect of a 6750-TEU (Twenty-foot Equivalent Unit) container ship. First, by comparing the heave, pitch, and vertical bending moment at midship section (VBM4) against experimental results reported in the literature, the validity of the numerical method in this paper is illustrated. Secondly, the ship responses under different wave length–ship length ratio, wave frequency-structure natural frequency, wave steepness, and ship speeds are studied. It is found that the wave length–ship length ratio has a more important influence on the hydroelastic response than that from wave frequency-structure natural frequency ratio, and the effect of wave non-linearity will behave differently under different wave length–ship length ratio. The increase of rigid body motion caused by forward speed will not correspondingly increase the non-linearity of the hydroelastic response.

Flow past a bluff body in freestream turbulence can substantially change the flow behaviour compared to that in smooth inflow. This paper presents the study of wake flow and aerodynamics of an oscillating square cylinder at the resonant frequency in freestream turbulence, with the integral length not greater than the cylinder side and the turbulence intensity not greater than 10%. Large eddy simulations (LES) in the Cartesian grid using the Immersed Boundary Method (IBM) technique embedded in a FVM solver, together with an efficient synthetic turbulent inflow generator implemented in an in-house parallel FORTRAN code are used for the study. The results are compared with those for smooth inflow, and relevant data published in the literature. The key findings are: the freestream turbulence conditions evidently reduces the local turbulent scales and fluctuations in the shear layer compared to in smooth flow, as small scale freestream turbulence breaks down cylinder-generated larger scale eddies and weakens them; but does not evidently affect the vortex shedding frequency, or the length of the recirculation region behind the cylinder. This suggests negligible change of drag coefficient compared to in smooth inflow. Moreover, this is because the vortex shedding is dominated by the forced oscillation at the resonance frequency, and the turbulence intensity is small.