An improved multi-phase WCSPH (Weakly Compressible Smoothed Particle Hydrodynamics) model has been established to numerically analyzethe2D sloshing phenomenon in a rectangular tank undergoing the forced rolling motion. The multiphase SPH model is applied taking care on combining the advantages of different SPH models. The application of artificial parameters is avoided in order to simulate physics phenomena realistically. The density re-initialization which is suitable for two-phase flow is applied to obtain smooth pressure field. A coupled dynamic solid boundary treatment (SBT) is adopted here to reduce numerical oscillations of pressure close to the boundary and to prevent particles' unphysical penetration into the solid boundary. Besides, in order to quantitatively study the wave elevation, a wave elevation measurement method based on linear interpolation is proposed.


Sloshing is a typical fluid-structure coupling flow phenomenon with strong nonlinearity and randomness, which is involved in many fields such as marine engineering, aerospace engineering and nuclear engineering, and so on. For instance, in the process of liquefied natural gas and oil transportation, the sloshing of liquid mineral fuels has bad effect on the structure safety of LNG tankers and FPSO vessels. A lot of work has been done for studying the sloshing problem using different methods including the model test (Bass et al., 1985, Liu and Lin, 2009, Pistani and Thiagarajan, 2012), theoretical analysis (Faltinsen, 1978, Faltinsen and Timokha, 2009, Chen et al., 2015) and numerical calculation (Armenio and Rocca, 1996, Wu et al., 1998, Frandsen, 2004).

SPH method which is an effective mesh-free method has been widely concerned for its natural advantages in solving sloshing problems. In SPH, physical objects are represented by a set of particles with individual masses. One particle interacts with nearby ones within a finite area called support domain, and the influence of the neighboring particles depends on the weight function or the smoothing function. The density and the acceleration of the particle are obtained by solving the governing equations descretized according to SPH algorithm (Liu et al., 2004). Much work has been done to improve the efficiency and accuracy for solving the sloshing problem with SPH method. Liu et al. (2012) proposed a kernel gradient correction and a coupled dynamic solid boundary treatment (SBT) which show great advantages in single phase sloshing problems. Chen et al. (2013) presented a boundary pressure correction to improve the measurement precision of the pressure field in boundary origin. Chowdhury and Sannasiraj (2014) compared the effects of different diffusive terms in sloshing problems. Bouscasse et al. (2014) studied the sloshing phenomenon in shallow water with experiment and numerical method of SPH. Delormeet al. (2009) studied the pressure field at the wall with SPH method.

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