High-Order WENO Schemes with an Immersed Boundary Method for Shallow Water Equations on the Tsunami Mitigation with Configurations of Cylinder Array

In this paper, we investigated the flow around vertical circular cylinders with the numerical simulation of shallow water equations. Since tsunami tidal waves have large potential energy due to height difference, the man-made structures near coast are heavily damaged during the propagation of waves. For the damage mitigation of natural disaster, a careful configuration of such obstructive structures is worthy of attention, and it is of great practical importance to provide numerical simulation based on the ideal models of natural or artificial structures in a coastal area. The simplified numerical models are listed as the single large cylinder and four small cylinders of double inline, double staggered, and single four arrangement with fixing the same blockage ratio. Among various up-to-date schemes, the fifth-order WENO scheme is selected with a ghost-cell immersed boundary method, which enabled the easy detection of the arbitrary body shapes emerged in background Cartesian grids. In addition, we proposed the non-reflecting characteristic boundary condition based on the characteristic compatibility equations derived in shallow water equations to suppress the unexpected reflection waves at the open boundary. The analysis on a benchmark problem on solitary wave reflection led to an expected validation with the present numerical model. Finally, reflection and diffraction of a tsunami wave are analyzed against a single and four cylinders of the same blockage density, and it is believed to reduce 20.80% points for the best case of single four cylinders in the view of dissipation ratio defined by the kinematic power.