Study on vertical line source Green's function for hydrodynamic calculations of ocean structures in water with ice cover

The numerical calculation of panel integrals associated with the Green's function satisfying water surface condition with ice cover is the basis for the boundary element method (BEM) to solve hydrodynamic problems of ocean structures in ice regions. In order to simplify the calculation process and reduce the time consuming, the vertical line source representing the analytical integral of ice-covered Green's function over vertical line segment is firstly derived in this paper. Then a semi-analytical quadrature, which accumulates a series of vertical line sources distributing along the horizontal direction, can be derived for the panel integral. In the numerical implementation, the asymptotic analysis method is employed to eliminate the singularity at zero point of the denominator, variable substitution is performed to treat the integral at infinite and approximate polynomials are introduced to evaluate the Bessel functions. Through the calculations of vertical line and panel integrals of Green's function and its derivatives, the analytical expression of vertical line source is proved to be accurate and more efficient than the normal numerical quadrature. Based on this, a BEM program is developed and applied in the hydrodynamic calculations of submerged structures with ice cover. The computed results are found to be in excellent agreement those of the validated BEM based on point source, which further verifies the reliability and practicability of utilization of vertical line source.