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Abstract
In this study, we derive a new set of depth-integrated models for solving unsteady flows that satisfy the Euler equations and nonlinear free surface boundary conditions in the sigma -coordinates. One of the obvious differences between the present approach and the ones directly solving the 3D Euler equations using Finite Element Method (FEM) is that in the present model the vertical velocity and the pressure field are eliminated by integrating the continuity equation and vertical momentum equation, respectively. Therefore, the present models only solve the horizontal velocity components and the free surface displacement in the two-dimensional horizontal (2DH) space. The new models are also more advantageous in using fewer elements in the vertical direction while achieving better performance. At this stage, the capability and application of the new models in dealing with free surface wave propagation problems are addressed.
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