Numerical diffusion and dissipation in hydrostatic models of internal waves

by Ben R. Hodges and Sarah Kelly Delavan

Hodges, B.R, and S.K. Delavan, Numerical diffusion and dissipation in hydrostatic models of internal waves, 17th ASCE Engineering Mechanics Conference, June 13-16, 2004, University of Delaware, Newark,, Electronic Proceedings (CD-ROM), 7 pgs.

Abstract

Analysis of numerical diffusion and dissipation rates in a hydrostatic model of an internal wave are used to illustrate convergence problems associated with hydrostatic modeling of an essentially non-hydrostatic phenomenon. As the model grid is refined in the vertical direction, the numerical diffusion is convergent (i.e. reduces with grid refinement). However as the model grid is refined in the horizontal direction, the diffusive error increases with grid refinement. The error behavior is linked to the development of shorter wavelength horizontal waves that are numerically generated as the internal wave steepens. Higher grid refinement in the horizontal direction allows shorter wavelengths to be developed, which have higher rates of numerical diffusion and dissipation. It is seen that the onset of the shorter wavelengths coincides with a shift in the diffusion and dissipation behavior that is highly grid-dependent.

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