论文标题
带床的连续运输的分散波水力动力学模型的不连续的galerkin方法
Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport
论文作者
论文摘要
提出了将绿色 - 纳格迪方程（流体动力学部分）与沉积物连续性Exner方程（形态动力学部分）耦合的色散水力多形动力学模型。提出了基于模型中不连续的Galerkin有限元离散化的数值解算法。该算法分别包括耦合和解耦方法，用于分别彼此同时和分开求解流体动力学和形态动力学部分。 Strang操作员分裂技术被用来分别处理分散术语，并提供了忽略指定区域（例如冲浪区）中的分散术语的能力。提出了可以处理湿干和检测波破裂的算法。用数值实验验证了数值溶液算法，以证明算法准确解析孤立波和常规波的流体动力学的能力，并通过此类波引起的形态动力学变化。结果表明，该模型有可能将其用于分散水波驱动的沿海形态动力学研究，因为流体动力学部分可以通过足够的精度解决水运动和分散波效应，并且可以捕获形态动力学模型，并且可以捕获床落生和层的主要特征。
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.
