Nonlinear liquid sloshing dynamics: Post-processing of conventional finite element solutions by digital filters

The aim of this study is to develop a robust finite element procedure for solving 2D and 3D nonlinear liquid sloshing dynamics modelled by standard potential theory. A computational problem encountered in almost all of the nonlinear simulations of inviscid free-surface flows is the appearance of "saw-tooth " spurious oscillations on the free surface as the waves become steep. The proposed post-processing, based on the moving least-squares smoothing algorithm, allows robust recovering more accurate nodal values of potential velocity gradients from conventional finite element solutions. Sloshing motions induced by harmonic and El-Centro seismic excitations are presented for small to steep non-overlapping waves in rectangular containers. The paper compares between various techniques to enhance stability and mitigate numerical oscillations, both common and innovative for sloshing problems. We explore the influence of these techniques on the free surface and velocity and pressure profiles, and choose the most robust stabilized finite element formulation for potential flow sloshing models.