The momentum conservative scheme for simulating nonlinear wave evolution and run-up in U-shaped bays

This paper investigates a previously developed numerical algorithm; the scheme solves Saint-Venant type equations as a quasi-1-dimensional model for wave dynamics in U-bays. The first validation uses the N-wave initial surface in a parabolic bay; numerical surface and horizontal velocity on the shoreline agree well with analytical results. Furthermore, simulation of N-wave shoaling phenomenon in a parabolic bay agree well with the analytical run-up and run-down heights. In the wind set-up and set-down simulations, numerical results show good agreement with analytical prediction in terms of surface elevation and velocity at the shoreline. Next, we discuss general U-bays with two types of influx: solitary and monochromatic waves; good agreement with analytical formula is obtained for U-bays with various m. All of the preceding observations indicates the robustness of our momentum conserving staggered-grid (MCS) scheme to describe wave dynamics in U-bays.