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.
翻译:在本研究中,提议了一个数字模型,保留一类非三相稳定状态解决办法,以预测波浪的传播和波浪在沿海地带的不断涌动。数字模型以圣维南系统为基础,并附有来源条件,因为底地地形和床面摩擦效应各有不同。由此产生的非线性系统在无结构三角网格上采用戈杜诺夫型有限体积方法来解决。对解决办法进行特殊的片分线性重建,同时采用纠正技术,以确保方法的准确性和计算水深的假定性。摩擦术语的有效半隐蔽技术以及底地表学的平衡配方被用来准确保存固定状态稳定状态解决办法。此外,我们证明数字系统保留了非三角稳定状态解决办法的类别。为了对照无结构的三角网格来验证拟议的数字模型,我们首先展示了它保存非三角稳定状态解决办法的能力,然后我们模拟了数个实验室实验,以预测浮浅的海滩上波浪流。数字模拟与实验室实验十分一致,这些实验证实了预测海浪的可靠性和准确性。