The Time-Domain Green Function Method Involving Fluid Viscosity

The source strength of near the water panels is divergent in dealing with large flaring surface ship by time-domain Green function method. The solution to the classical Cauchy-Poisson problem of water waves generated by an impulsive disturbance under the pure-gravity effect also presents a perplexing peculiarity. The surface elevation in a region approaching to the impulsive disturbance is found to diminish continuously in length and to increase continuously in height without limit. Based on these mathematic singularities, a new time-domain Green function method involving viscosity is studied by separating the regular part of the linear Navier-Stokes equation. Compared to the time domain potential theory, it is more realistic by including the fluid viscosity. The pressure can be obtained directly from the regular part.This paper is focused on the theory of time-domain Green function method involving fluid viscosity. And then, the method is applied to deal with the singular phenomena of large flaring surface ship when not considering viscosity. For this reason, the following problems are emphatically investigated.Firstly, time domain Green function method is introduced, including the boundary integral equation method and the evaluation of Green function.Secondly, the potential function involving viscosity is separated from linear Navier-Stokes equation, and the potential flow which is Green-function involving viscosity due to a point source is studied. A new boundary integral equation about the potential function involving viscosity is obtained.Thirdly, a numerical algorithm for the Green function involving viscosity is presented. The steepest decent method is used to deal with the high oscillating integral. At last, the hydrodynamics of a hemisphere and a cone is considered by time-domain Green function method involving fluid viscosity, comparing with the result of potential theory without viscosity.