The present work concerns a nonlinear numerical model of a sloshing experiment which consists of a gravity water wave inside a rectangular tank. At a certain time instant the free surface is shaped such that it entraps an air pocket close to the upper left corner of the tank. The air pocket is compressed and starts to oscillate. The pressure oscillations in the air pocket resemble the free oscillations of a single degree of freedom under-damped mass-spring system. The time before the wave touches the roof is modeled by a new numerical method called the boundary-element finite-difference method. This is a two-phase numerical method, designed to model the interaction effect between the escaping air and the water prior to impact. Both the water and the air are assumed incompressible and inviscid. The water flow is assumed irrotational and two dimensional and the air flow is assumed quasi-one-dimensional. Through different test cases the results from the new numerical method is compared with a linear analytical solution, a nonlinear multimodal solution and experimental results. The second part of the experiment, which is after the wave touches the roof and the air pocket is entrapped, is modeled using a mixed Eulerian-Lagrangian method. The air inside the air pocket can be assumed uniform in space. The air pocket is then modeled using a polytropic gas law. The water flow is described by potential flow theory. The results from the numerical model of the air pocket oscillations are compared with experiments. The comparison shows that the numerical model overestimates the maximum pressure inside the air pocket by 17%.
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