Lagrangian modelling of fluid sloshing in moving tanks

The paper considers the problem of sloshing of incompressible fluid in a moving 2-D rectangular tank under horizontal and vertical excitation. The problem is solved in Lagrangian variables by applying two approaches. First, a third-order asymptotic solution for resonant sloshing with a dominant mode is derived using a recursive technique. Then, fully nonlinear set of equations in the material coordinates is solved numerically by employing a finite difference method. Both methods are applied to a problem of high amplitude resonant Faraday waves and the obtained results are compared with experimental data known from the literature and a good agreement between the results of the two methods and the empirical data is demonstrated.