Reducing horizontal diffusion errors in σ-coordinate coastal ocean models with a second-order Lagrangian-interpolation finite-difference scheme
Date of Original Version
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. © 2002 Elsevier Science Ltd. All rights reserved.
Huang, Wenrui, and Malcolm Spaulding. "Reducing horizontal diffusion errors in σ-coordinate coastal ocean models with a second-order Lagrangian-interpolation finite-difference scheme." Ocean Engineering 29, 5 (2002): 495-512. doi:10.1016/S0029-8018(01)00036-1.