Adaptation of f-wave finite volume methods to the Boonkasame-Milewski non-Boussinesq two-layer shallow interfacial sloshing equations coupled to the vessel motion

A numerical method is proposed based on the high-resolution f-wave finite volume methods due to Bale et al. (2002) for the reduced two-layer inviscid, incompressible and immiscible shallow interfacial sloshing equations with a rigid-lid in the non-Boussinesq limit due to Boonkasame and Milewski (2011) The horizontal surge forcing function is added to the fluid equations. Numerical simulations are presented for the sloshing waves in a stationary vessel and also for the sloshing equations in a vessel under a prescribed surge forcing function. The proposed non-Boussinesq two-fluid finite volume solver is coupled to a Runge-Kutta solver for the vessel motion which is free to undergo horizontal motion governed by a nonlinear spring. The coupled numerical solutions with simulations near the internal 1:1 resonance are presented. Of particular interest is the partition of energy between the vessel and fluid motion. The new solvers are fast, stable, to machine accuracy, and can cover a wide range of parameters. The motivation is modeling of ocean wave energy harvesters.