论文标题
保留非平凡稳态解决方案的数值模型，用于预测沿海地区的波动
A numerical model preserving nontrivial steady-state solutions for predicting waves run-up on coastal areas
论文作者
论文摘要
在这项研究中，提出了一个保留一类非平凡稳态溶液的数值模型，以预测波浪的传播和海岸上的波动。数值模型基于具有源术语的圣人系统，这是由于可变的底部地形和床摩擦效应而导致的。使用godunov型有限体积方法在非结构化三角网格上解决了所得的非线性系统。通过校正技术实施了解决方案的特殊分段线性重建，以确保该方法的准确性和计算水深的阳性。摩擦项和底部地形的均衡配方的有效半图像技术用于确切保留固定的稳态S溶液。此外，我们证明数值方案保留了一类非平凡稳态解决方案。为了验证提出的数值模型针对实验，我们首先证明了其保留非平凡稳态溶液的能力，然后我们对几个实验室实验进行了建模，以预测在倾斜海滩上的波浪。数值模拟与实验室实验非常吻合，该实验证实了拟议的数值模型在预测沿海地区传播波的稳健性和准确性。
In this study, a numerical model preserving a class of nontrivial steady-state solutions is proposed to predict waves propagation and waves run-up on coastal zones. The numerical model is based on the Saint-Venant system with source terms due to variable bottom topography and bed friction effects. The resulting nonlinear system is solved using a Godunov-type finite volume method on unstructured triangular grids. A special piecewise linear reconstruction of the solution is implemented with a correction technique to ensure the accuracy of the method and the positivity of the computed water depth. Efficient semi-implicit techniques for the friction terms and a well-balanced formulation for the bottom topography are used to exactly preserve stationary steady-state s solutions. Moreover, we prove that the numerical scheme preserves a class of nontrivial steady-state solutions. To validate the proposed numerical model against experiments, we first demonstrate its ability to preserve nontrivial steady-state solutions and then we model several laboratory experiments for the prediction of waves run-up on sloping beaches. The numerical simulations are in good agreement with laboratory experiments which confirms the robustness and accuracy of the proposed numerical model in predicting waves propagation on coastal areas.
