Slosh Dynamics of Liquid Filled Rigid Containers: Two Dimensional Meshless Local Petrov Galerkin Approach
AbstractThis paper presents some of the interesting effects arising from the nonlinear motion of the liquid free surface, due to sloshing, in a partially filled rigid container subjected to forced excitation. A two dimensional meshless local Petrov Galerkin method is used for the numerical simulation of the problem. A local symmetric weak form (LSWF) for nonlinear sloshing of liquid is developed, and a truly meshless method, based on LSWF and moving least squares (MLS) approximation, is presented for the solution of the Laplace equation with the requisite time dependent boundary conditions. The MLS approximation with linear basis as well as Gaussian type weight function is employed in the computation. At every instant of time, velocity potential is computed at each node and the nodal positions are updated. The choice of a suitable scaling parameter value in the MLS approximation is discussed in this study. The effectiveness of the developed algorithm is demonstrated through a few numerical examples. The a.