考虑推移质输移的色散波水动力模型的间断Galerkin方法
Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport
摘要：
本文提出了一个将Green-Naghdi方程（水动力部分）和泥沙连续性Exner方程（地貌动力部分）耦合的色散波水动力模型。提出了基于间断Galerkin有限元离散的模型的数值解算法。该算法包括耦合和解耦的方法来解决的流体动力学和形态动力学的部分，同时和彼此分开，分别。Strang算子分裂技术被用来单独处理色散项，它提供了忽略指定区域（如碎波带）中色散项的能力。提出了能够处理湿-干和检测波浪破碎的算法。通过数值实验验证了该数值解算法的有效性，证明了该算法能够准确地求解孤立波和规则波的流体动力学问题，以及由孤立波和规则波引起的地形动力学变化。结果表明，该模型具有潜在的用于色散水波驱动的海岸地貌动力学的研究，鉴于水动力部分解决了水的运动和色散波的影响，具有足够的精度到冲区，和地貌动力学模型可以捕捉到的主要特点，床冲和沉积。
英文摘要：
A dispersive wave hydro-morphodynamic model coupling the Green-Naghdi equations (the hydrodynamic part) with the sediment continuity Exner equation (the morphodynamic part) is presented. Numerical solution algorithms based on discontinuous Galerkin finite element discretizations of the model are proposed. The algorithms include both coupled and decoupled approaches for solving the hydrodynamic and morphodynamic parts simultaneously and separately from each other, respectively. The Strang operator splitting technique is employed to treat the dispersive terms separately, and it provides the ability to ignore the dispersive terms in specified regions, such as surf zones. Algorithms that can handle wetting-drying and detect wave breaking are presented. The numerical solution algorithms are validated with numerical experiments to demonstrate the ability of the algorithms to accurately resolve hydrodynamics of solitary and regular waves, and morphodynamic changes induced by such waves. The results indicate that the model has the potential to be used in studies of coastal morphodynamics driven by dispersive water waves, given that the hydrodynamic part resolves the water motion and dispersive wave effects with sufficient accuracy up to swash zones, and the morphodynamic model can capture the major features of bed erosion and deposition.
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