In this paper, we use the multiple scale Trefftz method (MSTM) combined with the Lie group scheme to simulate the two-dimensional nonlinear sloshing problem. When considering the effects of baffles for the nonlinear sloshing phenomena, the conventional Trefftz method (CTM) may encounter numerical instabilities, degenerate scale, and numerical dissipation problem. In order to eliminate the high-order numerical oscillations and noise disturbances on the boundary, the vector regularization method (VRM) and the multiple scale characteristic lengths (CLs) are applied. At the same time, they can also overcome the degenerate scale problem. Additionally, in order to increase the numerical accuracy at the initial-boundary value problem, we introduce the weighting factors based on the Lie group scheme into the linear system to avoid high numerical dissipation and reduce the numbers of iterations. Comparing with the solutions in the previous literature, the present scheme is efficient and accurate in simulating nonlinear sloshing problem of the two-dimensional tank with baffles. Hence, the method developed here is a simple and stable way to cope with the nonlinear sloshing problem with baffles.


Liquid sloshing in a moving container has been studied in various engineering problems, such as liquid propellant launch vehicles (Mohammad et al., 2011), oil surges in large tanks due to long-term intense ground motion (Tetsuya and Takashi, 2013), and shock surges in nuclear fuel pools (Eswaran and Reddy, 2016). Besides, the sloshing effect in the ship's ballast tanks may cause it to experience large rolling moments, even losing dynamic stability and overturning (Przemysáaw et al., 2012). Also, if the forcing frequency coincides with the natural sloshing frequency, the high dynamic pressures, by reason of resonance, may damage the tank walls and may even create moments that affect the stability of the vehicle. Therefore, the hydrodynamics of sloshing for the vehicle is important and requires understanding sloshing dynamics phenomena.

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