Moving shoreline boundary condition for nearshore models |
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| Authors: | R S Prasad I A Svendsen |
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| Institution: | Department of Civil Engineering, College of Engineering, CACR, University of Delaware, 137 DuPont Hall, Newark, DE 19716, USA |
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| Abstract: | The paper develops and analyzes two fully nonlinear boundary conditions that incorporate the motion of the shoreline in nonlinear time domain nearshore models. A moving shoreline essentially means the computational domain is changing with the solution of the flow. The problem is solved in two steps. The first is to establish an equation that determines the motion of the shoreline based on the local momentum balance. The second is to develop and implement into a shoreline model the capability of accommodating a changing computational domain. The two models represent two different ways of addressing this step: one is to track the position of the shoreline in a fixed grid by establishing a special shoreline point which generally is not a fixed grid point. The second is by a coordinate transformation that maps the changing domain onto a fixed domain and solves the basic equations in the mapped domain. The two shoreline conditions are tested against three known solution for nonlinear shoreline motion. Two are the 1-D solutions to the nonlinear shallow water (NSW) equations by Carrier and Greenspan J. Fluid Mech. 4 (1958) 97], one representing the response to a transient change in the offshore water level, the other the motion due to a periodic standing wave, both on slopes steep enough to allow full reflection. The third is the 2-D horizontal (2DH) computational solution by Zelt Coast. Eng. 15 (1991) 205] for the run-up of a solitary wave on a cusped beach. In all cases, both models are shown to behave well and give high accuracy results for suitably chosen grid and time spacings. |
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| Keywords: | Shoreline condition Numerical modeling Fixed grid Domain mapping |
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