Difference between revisions of "Biharmonic"
From MohidWiki
| (8 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | The biharmonic | + | The biharmonic filter is an extra term that is added in the horizontal turbulent viscous flux, '''J''', that filters high frequency oscillations in a numerical model of advection-diffusion of a property <math>C</math>(i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution): |
<math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math> | <math>\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right) </math> | ||
| − | A ready made formula that would estimate the order of magnitude of the | + | where <math>\mathrm{K}</math> is Fick's law diffusivity. |
| + | A ready made formula that would estimate the order of magnitude of the <math>\kappa_4</math> coefficient for momentum would be | ||
<math>\kappa_4 \sim \frac{U}{16} \Delta x^3</math> | <math>\kappa_4 \sim \frac{U}{16} \Delta x^3</math> | ||
| + | |||
| + | where U is a typical flow velocity and <math>\Delta x</math> is the numerical model horizontal resolution. | ||
| + | |||
| + | ==MOHID== | ||
| + | In mohid, you need to add in the Hydrodynamic_x.dat the following keywords: | ||
| + | |||
| + | BIHARMONIC : [0/1] <-- Activates de biharmonic viscous flux | ||
| + | BIHARMONIC_COEF : [Real] <-- Sets the value of <math>\kappa_4</math> | ||
==References== | ==References== | ||
Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing. | Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing. | ||
Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002. | Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002. | ||
| + | |||
| + | [[Category:MOHID]] | ||
| + | [[Category:Hydrodynamic]] | ||
Latest revision as of 15:30, 28 June 2011
The biharmonic filter is an extra term that is added in the horizontal turbulent viscous flux, J, that filters high frequency oscillations in a numerical model of advection-diffusion of a property 
(i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):
where 
is Fick's law diffusivity.
A ready made formula that would estimate the order of magnitude of the 
coefficient for momentum would be
where U is a typical flow velocity and 
is the numerical model horizontal resolution.
MOHID
In mohid, you need to add in the Hydrodynamic_x.dat the following keywords:
BIHARMONIC : [0/1] <-- Activates de biharmonic viscous flux BIHARMONIC_COEF : [Real] <-- Sets the value of
References
Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing. Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002.
