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This work presents a study of the influence of the filling level on the wave pattern during a sloshing problem. To this end, a rectangular tank of aspect ratio 2:1 is mounted on a shake table subject to controlled external motions. A frequency sweep analysis is performed nearest to the primary resonance frequency using two different amplitudes of imposed motion and different water depths. The wave evolution is registered at certain control points. In particular, this work is devoted to identifying the effect of the filling level on the dynamics of the wave patterns, emphasizing the nonlinearities of the free surface and their dependence on the water depth. The free surface measurements are compared with those obtained from a fixed mesh finite element simulation of the Navier-Stokes equations. The free surface is tracked using a Lagrangian technique. The effect of the bottom boundary conditions on the wave pattern is also evaluated from these simulations. From the experiments, it is confirmed that maximum and minimum wave heights do not change for larger water depth, i.e., when deep water conditions are fulfilled. This fact is also reflected by the numerical results. The computed wave evolution satisfactorily matches the experimental data. In addition, analytical solutions obtained using a potential flow approach are also evaluated. They fail in the description of nonlinear responses, but their coefficients can be numerically or experimentally characterized to fit more realistic solutions. [ABSTRACT FROM AUTHOR]

This work encompasses numerical and experimental studies of three-dimensional (3D) sloshing problems. The two-fluid viscous flow, which is solved within a stabilized finite element context, involves liquid and gaseous phases. The free surface is captured with a level set (LS) method, including the bounded renormalization with continuous penalization technique, to avoid the well-known spreading of the marker function. Specifically, this technique is improved with a volume-preserving algorithm for long-term analyses. To verify the numerical model, the responses of free-sloshing cases are compared with analytical solutions and other results computed using a Lagrangian technique. These simulations assess the influence of considering two-dimensional (2D) and 3D analyses, as well as the effects of depth and viscosity. This work presents data obtained from a forced sloshing experiment that is specifically devoted to 3D free surface behaviour. Free surface evolution measurements are used to validate the numerical method. Moreover, the effect of the initial conditions used to promote 3D behaviour in the modelling is evaluated. [ABSTRACT FROM AUTHOR]