Numerical simulation of the two-dimensional sloshing problem using a multi-scaling Trefftz method

Here, we develop a multi-scaling Trefftz method (MSTM) for the Laplace equation associated with the group-preserving scheme (GPS) to describe nonlinear sloshing behavior of the incompressible, non-viscous, and irrotational fluid. Chen et al. [29] proposed that the characteristic length of the Trefftz method and the concept of controlled volume could be used to overcome numerical errors and dissipation in the simulation of the sloshing problem. However, the nonlinear dependence of the characteristic length on initial conditions was neglected in the numerical development. In addition, this study presents a numerical method with automatically adaptive computational steps for describing the nonlinear sloshing behavior as well as for satisfying the conservation of mass at each time step. The method developed here presents a simple and stable way to cope with the nonlinear sloshing problem.