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Application of Trefftz-type boundary element method to simulation of two-dimensional sloshing phenomenon

机译：Trefftz型边界元法在二维晃荡现象模拟中的应用

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摘要

This paper describes the application of Trefftz method to the simulation of sloshing phenomenon on the fluid in two-dimensional vessel. The phenomenon is governed by the Laplace equation with respect to the velocity potential. The equation is solved with the adequate boundary conditions in order to estimate potential derivatives on liquid free surface. The free surface profile and the boundary condition on the surface are updated with the derivatives. Since, in Trefftz method, the potential is approximated with the superposition of the regular T-complete functions, their direct differentiation leads to the derivatives. Trefftz method, moreover, can estimate easily not only the first-derivative but also the second-derivative of the potential function. Therefore, we will discuss more accurate estimation scheme of the sloshing phenomenon using both derivatives. Finally, the present method is applied to the simulation of the sloshing phenomenon of the fluid in the rectangular vessel.
机译：本文介绍了Trefftz方法在二维容器中流体晃荡现象模拟中的应用。该现象由关于速度势的拉普拉斯方程控制。用适当的边界条件求解该方程，以便估计无液表面上的潜在导数。用导数更新自由表面轮廓和表面边界条件。由于在Trefftz方法中，势是通过规则T-完全函数的叠加来近似的，因此它们的直接微分导致了导数。此外，Trefftz方法不仅可以轻松估计势函数的一阶导数，而且可以轻松地估计其二阶导数。因此，我们将讨论使用这两种导数的更准确的晃动现象估计方案。最后，将本方法应用于矩形容器中流体晃荡现象的模拟。

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