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Reducing Numerical Diffusion Effects with Pycnocline Filter
by Bernard Laval, Ben R. Hodges and Jörg Imberger
Citation: Laval, B., B.R. Hodges, and J. Imberger, "Reducing Numerical Diffusion Effects with Pycnocline Filter." Journal of Hydraulic Engineering 129: (3): 215-224 (2003).
Abstract
Numerical or artificial diffusion is the unintentional smoothing of gradients associated with the discretization of the transport equations. In lakes and reservoirs where through-flow is small, the effects of numerical diffusion of mass are cumulative, leading to a progressive weakening of vertical density stratification. This density field misrepresentation precludes accurate, long-term, three dimensional (3D), hydrodynamic simulations on fixed grids in closed basins with an active thermocline. An ad hoc technique to limit the destratifying effects of numerical diffusion of mass is presented and tested for a 3D, hydrostatic, Z-coordinate numerical model. The technique quantifies the domain-integrated numerical diffusion by assessing the change in the background potential energy E_b . At each time step, the change in E_b associated with numerical diffusion is calculated, then removed using a sharpening filter applied to each water column. In idealized test cases, the filtering technique is effective in maintaining density stratification over one year while undergoing periodic, large-amplitude forcing by internal waves. Forty-day simulations of Lake Kinneret compared to field measurements demonstrate improved representation of density stratification using the filtering technique.
| ©2003 Ben R. Hodges | • last updated August 16, 2003 |
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