Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method

Analysis on Shift of Nature Modes of Liquid Sloshing in a 3D Tank Subjected to Oblique Horizontal Ground Motions with Damping Devices

“…In this way, the computational domain is invariant (eight unit squares), and the more advantage of the transformations is to deal with the tank with internal structures of various positions and scales and to avoid the internal structure surrounded by the irregular meshes. Furthermore, combining with the stretching technique [28], the stretching grids can be arranged around the structure boundaries with the sharp corners. The thickness of the baffle or plate is set only at 1% of the tank's length and is, therefore, negligible compared with the length of the tank.…”

“…All computations use the dimensionless equations in the --coordinate system. All the numerical results presented in this work are in the dimensionless form [28], and the dimensionless equations can be referred to [24,29] that are omitted in the text. Central difference approximations are used for the space derivatives, except at the boundary where the fictitious cell approach [24,27] is employed.…”

“…The Crank-Nicholson second order finite difference scheme and the Gauss-Seidel point successive overrelaxation iterative procedure are used to calculate the velocity and pressure, respectively. The detailed numerical scheme is similar to that reported [24,28,29] and is omitted here.…”

“…As a 3D baffled tank is subjected to oblique horizontal excitation, the coupled effect of nature modes of sloshing waves will be triggered. Wu and Chen [28,29] reported that the types of sloshing waves in a 3D tank under various excitation angles and frequencies are the single-directional wave, square-like wave, swirling wave, and irregular wave, and these waves can be triggered by the specific excited frequencies of 0.9 1 , 1.5 1 , 1.0 1 , and 2 1 , respectively. In the following subsections, the effect of the baffle of a fixed height = 0.5 0 on the shift of natural modes of different types of sloshing waves for a 3D tank under oblique excitation is discussed in detail.…”

Pattern formation of parametrically driven surface waves induced by vibration

“…Both harmonic and subharmonic sloshing modes have been considered, among others, by Miles (1984), Funakoshi & Inoue (1988), Feng (1997), Hill (2003), and Faltinsen, Timokha, and collaborators (in a series of papers, see Faltinsen, Rognebakke & Timokha 2006, Hermann & Timokha 2008, and references therein) using modal expansions and considering fully nonlinear gravity waves under general excitation (not necessarily horizontal); Frandsen (2004) and Wu & Chen (2009), instead, addressed this problem using finite differences.…”