A three-dimensional Dirichlet-to-Neumann operator for water waves over topography
A three-dimensional Dirichlet-to-Neumann operator for water waves over topography
复制标题
地形上水波的三维狄利克雷-诺依曼算子
DOI：
10.1017/jfm.2018.241
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
A. Nachbin
中科院分区：
文献类型：
--
作者：
D. Andrade;A. Nachbin
表面水波被认为是在高度可变的非光滑地形上传播的。对于这个三维问题，构造了Dirichlet-to-Neumann(DTN)算子，简化了数值模拟和向二维自由面的演化。通过矩阵分解定义了相应的离散傅立叶积分算子。分解的地形部分需要特别注意，并相应地提供了Galerkin方法。沿着自由表面的一维数值模拟验证了在存在大幅度快速变化地形的情况下的DTN公式。另一种基于保角映射的方法被用于基准测试。在存在一个伦堡透镜(一个特定的水下土丘)的情况下的二维模拟说明了三维DTN算子的准确性能。
Surface water waves are considered propagating over highly variable non-smooth topographies. For this three-dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modelling and evolution to the two-dimensional free surface. The corresponding discrete Fourier integral operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care, and a Galerkin method is provided accordingly. One-dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large-amplitude rapidly varying topography. An alternative conformal-mapping-based method is used for benchmarking. A two-dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three-dimensional DtN operator.