Reducing horizontal diffusion errors in σ-coordinate coastal ocean models with a second-order Lagrangian-interpolation finite-difference scheme |
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Authors: | Wenrui Huang Malcolm Spaulding |
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Institution: | a Civil Engineering Department, FAMU-FSU College of Engineering, Tallahassee, FL 32310-6046, USA b Ocean Engineering Department, University of Rhode Island, Rhode Island, RI 02882, USA |
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Abstract: | When a steep bottom slope exists, it is well known that conventional methods for calculating horizontal diffusion in sigma-coordinate coastal ocean models causes spurious transport (e.g. salinity, temperature, and sediments) and currents. In this study, a second-order accurate finite-difference algorithm and program have been developed to reduce the spurious numerical diffusion errors. In the proposed algorithm, the finite differencing is performed in the x-z coordinate system to approximate the horizontal gradient. Each variable in the finite differential formation is calculated in the sigma-coordinate grid cells using a second-order Lagrangian interpolation polynomial. In conjunction with a stepwise bottom boundary condition, numerical experiments show that the proposed finite-difference scheme considerably reduces numerical errors compared to conventional approaches when dealing with horizontal diffusion over steep topography, which often occurs in coastal oceans and navigation channels. |
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Keywords: | σ-Coordinate Horizontal diffusion Three-dimensional Coastal ocean model |
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