Semi-Lagrangian numerical simulation method for tides in coastal regions

In this paper, a numerical computation method is proposed to simulate tides in coastal regions. The proposed method is based on the hyperbolic form of governing equations and employs a semi-Lagrangian scheme to ensure the accuracy and stability of numerical computations. Open and wall boundary conditions can be treated universally by combining them with the semi-Lagrangian scheme. Furthermore, the method is applied to some benchmark problems of shallow water to examine its performances in wave propagation, wave transparency through open boundaries, and tides in semi-enclosed bays. The results obtained demonstrate that the proposed method can be utilized as a practical tool to investigate tidal dynamics in coastal regions.