Finite Difference Based Sigma - Transformation Approach for Liquid Sloshing in a Rectangular Tank under Regular Wave Excitation

Abstract

In this paper, a fully non-linear finite difference model has been developed based on the inviscid flow equations, and a simple mapping function was used to remove the time-dependence of the free surface in the fluid domain. The time-varying fluid surface is mapped onto a rectangular domain by the Sigma (s )-transformation. This method is a simple way to simulate non-breaking waves quickly and accurately especially that has a low steepness. The fluid motion is solved in a unit square mesh in the transformed flow domain (i.e., computational domain). Difference between the peaks and troughs of waves are discussed for three different cases of horizontal (surge), vertical (sway) and combined excitations of off and at resonance frequency of the tank. The spectrum analysis of horizontally excited tank is presented. The stability and instability regions associated with vertical and combined excitations conditions are discussed with the plots of free surface elevation, phase-plane diagram and free surface profile.