论文标题
一般底部地形的Serre-Green-Naghdi模型的双曲重新印象
A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies
论文作者
论文摘要
我们提出了一种新型的双曲重新印象，以描述分散水波的描述。与经典的BousSinesQ型模型相反，它仅包含一阶导数，从而可以克服数值困难以及由高阶项产生的严重时间步长限制。当人造声速倾向于无穷大时，提出的模型将减少为原始的SGN模型。此外，它具有节能定律，当人造声速进入无限时，可以从中检索与原始SGN模型相关的能源保护定律。然后借助高阶Ader不连续的Galerkin有限元元件方案来解决偏微分方程的管理方程。对于平面和非平板底部的数值和实验结果，新模型已成功验证。对于具有较大变化的底部地形图，本文提出的新模型就SGN模型的双曲重新印度提供了更准确的结果，最近在“ C. Escalante，M。Dumbser和M.J. Castro中提出了轻度的底部近似值。
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to overcome the numerical difficulties and the severe time step restrictions arising from higher order terms. The proposed model reduces to the original SGN model when an artificial sound speed tends to infinity. Moreover, it is endowed with an energy conservation law from which the energy conservation law associated with the original SGN model is retrieved when the artificial sound speed goes to infinity. The governing partial differential equations are then solved at the aid of high order ADER discontinuous Galerkin finite element schemes. The new model has been successfully validated against numerical and experimental results, for both flat and non-flat bottom. For bottom topographies with large variations, the new model proposed in this paper provides more accurate results with respect to the hyperbolic reformulation of the SGN model with the mild bottom approximation recently proposed in "C. Escalante, M. Dumbser and M.J. Castro. An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes, Journal of Computational Physics 2018".
