An Explicit/Implicit Lie-group Scheme for Solving Problems of Nonlinear Sloshing Behaviors

Chen, Yung-Wei (National Taiwan Ocean University) | Shih, Chao-Feng (National Taiwan Ocean University) | Liu, Yu-Chen (National Taiwan Ocean University) | Soon, Shih-Ping (National Taiwan Ocean University)


This paper presents an equal-norm multiple-scale Trefftz method (MSTM) associated with the group-preserving schemes (GPS) to tackle some difficulties in nonlinear sloshing behaviors. The MSTM combined with the vector regularization method is first adopted to eliminate the higher-order numerical oscillation phenomena and noisy dissipation in the boundary value problem. Then, the weighting factors of initial and boundary value problems are introduced into the linear system to prevent the elevation from vanishing without iterative computational controlled volume. More important, the explicit scheme, based on the GL (n, R), and the implicit scheme can be combined to reduce iteration number and increase computational efficiency. A comparison of the results shows that the proposed approach is better than previously reported methods.


Sloshing of liquid in tanks has received considerable attention from many researchers in related engineering fields. The problem arises because excessive sloshing of the confined liquid can strongly damage the structure or the loads induced by sloshing, which may seriously modify the dynamics of the vehicle that supports the tanks—for example, fuel sloshing in liquid propellant launch vehicles (Lu et al., 2015), oil oscillations in large storage tanks as a result of long-period strong ground motions (Hashimoto et al., 2017), and sloshing in nuclear fuel pools owing to earthquakes (Eswaran and Reddy, 2016). Besides, sloshing effects in the ballast tanks of a ship may cause it to experience large rolling moments and eventually capsize because of loss of dynamic stability (Krata, 2013; Sanapala et al., 2018). Also, if the forcing frequency coincides with the natural sloshing frequency, the high dynamic pressures, by reason of resonance, may damage the tank walls. Thus, accurate prediction of sloshing behaviors in tanks driven by external forces is very critical for successful structural design and reducing impacts on vehicle maneuvering.