Slosh Dynamics of Liquid-Filled Rigid Containers: Two-Dimensional Meshless Local Petrov-Galerkin Approach

Application of the peridynamic differential operator to the solution of sloshing problems in tanks

“…As the development of computer technology, the use of numerical tools in the absence of analytical solutions has become increasingly popular. Linear and non-linear numerical approaches have been proposed to efficiently and accurately simulate the non-breaking waves in the sloshing problem (see for instance Boroomand et al, 2016;Boroomand et al, 2017;Chen and Nokes, 2005;Chen et al, 2007b;Frandsen, 2004;Pal, 2012;Ramaswamy and Kawahara, 1986;Shobeyri and Yourdkhani, 2017;Wu and Chang, 2011;Zandi et al, 2012;Zandi et al, 2017;Zhang et al, 2016a).…”

“…3 Non-linear liquid sloshing under harmonic excitation 5.3.1 Sloshing under resonant excitation. In this section, to get an insight into the accuracy, the solution of PDDO is compared with the solution of the Meshless Local Petrov-Galerkin (MPLG) approach (Pal, 2012). The parameters of the tank (Figure 8) are set as those chosen by Pal (2012) as H = 1.0 m and L = 2.0 m. The lowest natural angular frequency of the tank is v 0 = 3.76 rad/s (Pal, 2012).…”

“…In this section, to get an insight into the accuracy, the solution of PDDO is compared with the solution of the Meshless Local Petrov-Galerkin (MPLG) approach (Pal, 2012). The parameters of the tank (Figure 8) are set as those chosen by Pal (2012) as H = 1.0 m and L = 2.0 m. The lowest natural angular frequency of the tank is v 0 = 3.76 rad/s (Pal, 2012). A periodic cosine excitation with a shaking frequency of v = 1.0 v 0 is considered on the x direction as:…”

Simulation of two-dimensional sloshing phenomenon by generalized finite difference method

“…In order to get rid of time-consuming tasks of mesh generation and numerical quadrature, some so-called meshless methods have been proposed in the past decades, such as the MLPG method [10], the method of fundamental solutions [13][14], the MCTM [9,15], the element-free Galerkin method [16], the smoothed-particle hydrodynamics [17], the local RBFCM [18], the GFDM [19][20][21][22][23][24][25][26][27], etc. Among them, the GFDM is one of the most-promising domaintype meshless methods.…”

“…Consequently, numerical simulation is a good candidate in comparison with mathematical means and experimental study when academic research and engineering design related to sloshing phenomenon are considered. In the past decades, many numerical schemes [1][2][3][4][5][6][7][8][9][10] have been proposed to accurately and efficiently model the non-breaking waves in the sloshing problem, such as the finite difference method (FDM) [3], the finite element method (FEM) [4,5], the boundary element method [6], the radial basis function collocation method (RBFCM) [7], the Trefftz method [8], the modified collocation Trefftz method (MCTM) [9], the meshless local Petrov-Galerkin (MLPG) method [10], etc. For example, Frandsen [3] proposed a FDM scheme, combined with a modified sigma-transformation, to simulate non-linear sloshing wave motion in a two-dimensional tank.…”