Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves
Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves
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DOI：
10.1016/j.jcp.2014.06.035
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
E. Gagarina;V. Ambati;J. V. D. Vegt;O. Bokhove
中科院分区：
文献类型：
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作者：
E. Gagarina;V. Ambati;J. V. D. Vegt;O. Bokhove
基于势流近似，提出了一种新的求解非线性自由表面重力水波的变分有限元方法。这种方法还可以处理造波者产生的波。它的表述源于Miles的水波变分原理和空间连续、时间不连续的有限元离散。这种变分有限元方法的一个新特点是，自由面的演化依赖于网格的变形，而网格的变形在几何上依赖于自由面的演化。另一个关键特征是使用时间上的变分(Dis)连续Galerkin有限元离散。此外，在没有造波器的情况下，对于自由表面自由度，它等价于二阶辛STörmer-Verlet时间推进格式。这些关键特点增加了数值方法的稳定性。最后，用长时间模拟验证了所得到的数值方案与非线性解析解的一致性，并与荷兰海洋研究所波盆中的驱动波解的实验测量结果进行了验证。
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time. One novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis-à-vis the mesh deformation being geometrically dependent on free surface evolution. Another key feature is the use of a variational (dis)continuous Galerkin finite element discretization in time. Moreover, in the absence of a wave maker, it is shown to be equivalent to the second order symplectic Störmer–Verlet time stepping scheme for the free-surface degrees of freedom. These key features add to the stability of the numerical method. Finally, the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the Maritime Research Institute Netherlands.