| 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. |
