This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory. The boundary value problem is solved by the NURBS （non-uniform rational B-spline） higher-order panel method, in which a time-domain Green function is employed. The energy dissipation is modeled by changing the boundary condition on solid boundaries. Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion. Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other. It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.
The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.
