SUMMARYA three-dimensional numerical model based on the full Navier-Stokes equations (NSE) in -coordinate is developed in this study. The -coordinate transformation is ÿrst introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial di erentiation, a new set of governing equations is derived in the -coordinate from the original NSE deÿned in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23:485 -501), which splits the solution procedure into the advection, di usion, and propagation steps, is used to solve the modiÿed NSE. The model is ÿrst tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a conÿned tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two-and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction.
13When simulating urban floods, most approaches have to simplify the topography of the city and cannot 14 afford to include the obstacles located in the streets such as bus stops, trees, parked cars, etc. The aim of the 15 present paper is to investigate the error made when neglecting such singularities in a simple flooded 3-branch 16 crossroad configuration with a specific concern regarding the error in discharge distribution to the 17 downstream streets. Experimentally, the discharge distribution for 14 flows in which 9 obstacles occupying 18 1/6 of the flow section are introduced one after the other is measured using electromagnetic flow-meters. The
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