Simulation of sloshing motions in fixed and vertically excited containers using a 2-D inviscid σ-transformed finite difference solver

A numerical study of three-dimensional liquid sloshing in tanks

“…For example, Chen et al [3] adopted a curvilinear coordinate system to map the sloshing from the non-rectangular physical domain into a rectangular computational domain. Similar ideas have also been employed by Frandsen and Borthwick [13] and Frandsen [14], who conducted a series of numerical experiment in a 2-D tank which is moved both horizontally and vertically by using r-coordinate transformation. However, because of the use of potential flow assumption, both viscous sloshing and rotational motion of the liquid cannot be captured by the models introduced above.…”

Sloshing motions in excited tanks

“…The results herein are based on the first set of numerical tests done by Frandsen and Borthwick [16] who checked the sensitivity of the numerical scheme to the time step and grid resolution. Figs.…”

A numerical study: liquid sloshing dynamics in a tank due to uncoupled sway, heave and roll ship motions

“…The study explored the formation of standing wave, traveling wave, hydraulic jump and breaking wave under the influence of roll excitation frequency and amplitude for the various liquid filling levels. Frandsen (2003) developed a finite difference based numerical scheme and sigmatransformation mapping technique to simulate sloshing motion in the vertically excited containers. The importance of wave steepness on the initial perturbation and the associated nonlinear behaviour in free surface elevation has been discussed.…”