Interplay between grid resolution and pressure decimation in non-hydrostatic modeling of internal waves

Abstract

The Pressure Decimation and Interpolation (PDI) method is an effective numerical technique to improve the computational efficiency of a non-hydrostatic model. We carried out an analysis of the wave dispersion relation and quantitative measurements of numerical dissipation and diffusion affected by the PDI scheme in modeling of internal waves. The linear analysis on the wave dispersion relation shows that the accuracy in predicting wave dispersion depends highly on how well the vertical structure of the non-hydrostatic pressure is represented over depth. The accuracy is not only dependent on the resolution of the pressure grid, but also on the interpolation method. The third-order spline interpolation provides a more accurate wave dispersion relation than the lower-order (linear and quadratic) interpolation. Quantitative measurements of wave energy transfer from the basin-scale internal seiche to small-scale internal solitary waves, as well as numerical dissipation and diffusion in the PDI model, were performed in the simulation of internal waves. Results show that the resolution of the pressure grid has a major effect on the wave dispersion but a negligible effect on the numerical dissipation and diffusion. The velocity grid resolution has a significant influence on the numerical diffusion and a minor effect on the numerical dissipation.