Study on HOBEM Based on Analytical Panel Integrals Related to Translating-Pulsating Source for Hydrodynamic Responses of Vessels Sailing in Waves

A higher-order boundary element method(HOBEM)incorporated with analytical panel integrals related to translat-ing-pulsating source Green’s function is proposed for the hydrodynamic response prediction of ships advancing in waves.In this method,the 9-node bi-quadratic curvilinear elements employed to discretize the mixed-source/dipole boundary integral equation are mapped into the parametric plane through a coordinate transformation.Then in order to ease the numerical instability problem,a novel analytical quadrature is derived to calculate the influence coefficients by changing the integral order and using integration by parts.The singularity caused by infinite discontinuity is analyzed and eliminated by adopting some mathematical techniques.Through the calculations of panel integrals of Green’s function and its x-derivative,the analytical integral method is proved to be always accurate even for field points approaching the free surface,where numerical quadrature is impossible to give reasonable results.Based on this,a higher-order seakeeping program is developed and applied in the motion response prediction of two different types of ships(i.e.,a wall-sided ship Wigley III and a non-wall-sided ship S175).By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating and higher-order Green’s function methods based on traditional Gauss quadrature,it is found that the HOBEM based on analytical quadrature is of better accuracy and stability.For the non-wall-sided ship,only the present method can produce reasonable pre-diction of motion responses,while obvious oscillatory phenomenon is observed in the results of the other two numerical methods based on Gauss quadrature.

Numerical Simulation on Partially Liquid-Filled Sloshing with Baffle Under Different Density Ratios by the CLSVOF/IB Method

The density and viscosity ratios on partially liquid-filled sloshing with baffle have been investigated numerically in this study.As the key to success in the present simulation,the Coupled Level Set and the Volume of Fluid(CLSVOF)method and the Immersed Boundary(IB)method are used to capture gas/liquid and fluid/structure interfaces,respectively.Within the CLSVOF method,surface normal in weighting factors is calculated by the level set function,resulting in a more accurate solution.Furthermore,the Tangent of Hyperbola for INterface Capturing(THINC)coupled with the Weighted Linear Interface Calculation(WLIC)scheme is used for capturing moving interface.As a standard practice,we first validate the code by comparing it with experimental results of liquid sloshing,which involves large deformation of interface.In addition to the validation study of the present method,the problems of liquid sloshing with baffle are investigated to understand kinematics and dynamics behaviors under different density and viscosity ratios.

Numerical Simulation of Tsunami-Like Wave Impacting on Breakwater by CLSVOF/IB Method

In the current study,the treatment of air/water interface has been made on dam-break induced tsunami-like wave by the Coupled Level Set and Volume of Fluid(CLSVOF)three-dimensional modelling.The overall CLSVOF method adopts a Tangent of Hy-perbola for INterface Capturing(THINC)scheme with the Weighted Linear Interface Calculation(WLIC)and Level Set(LS)function for capturing interface and calculating normal vector,respectively.As far as THINC/WLIC scheme is concerned,since the convection problem of the VOF function can be solved well,the numerical diffusion can be avoided.The spatial terms in the LS equation were discretized by the Optimized Compact Reconstruction Weighted Essentially Non-Oscillatory(OCRWENO)scheme with fourth-order accuracy,which can avoid false oscillation of LS solution.By combining CLSVOF method with Immersed Boundary(IB)method,the simulation of dam-break induced tsunami-like wave impacting on a stationary breakwater can be carried out.Grid sensitivity,mass error and free-surface profile are first calculated for the tsunami-like wave problem to validate the proposed numerical algorithm,which shows excellent agreement between the numerical results and experimental data.Tsunami-like waves with varied tailgater levels are then investigated.Calculations of velocity magnitude,free-surface profile and wave elevation of the tsunami-like wave are conducted to investigate its dynamics and kinematics.