Improved Efficiency in a Finite-difference, σ-coordinate, Free-surface Non-hydrostatic Ocean Model

The increasing demand for the investigation of non-hydrostatic effects in coastal ocean modeling requires non-hydrostatic ocean models, for example the research on internal solitary waves and dispersion surface waves. However, the use of non-hydrostatic ocean models has been restricted by their expensive numerical cost compared to hydrostatic models, because of the version of large and sparse matrix in the Poisson equation of non-hydrostatic pressure, especially the ocean models in σ-coordinates. In order to improve efficiency, the Poisson equation in a finite-difference, σ-coordinate, non-hydrostatic ocean model is simplified and the number of non-zero elements in the matrix is reduced, through some approximated treatment to the σ-direction gradient terms. The validation of five test cases including surface waves and internal waves modeling showed that, the model with simplification algorithm was stable and generated identical results to simulations with original algorithm, while the execution CPU time decreased ~40%, demonstrating a evident promotion to computational efficiency. And this simplified method can also be easily applied to other non-hydrostatic models in σ-coordinate.