CMS-Flow:Subgrid Turbulence Model: Difference between revisions

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where  <math>\nu_{0}</math> is a base value approximately equal to the kinematic viscosity, <math>c_0</math> is an empirical coefficient, <math>c_{sm}</math>  is an empirical coefficient (Smagorinsky coefficient), <math> \Delta </math> is the local cell area, and <math>|S|</math> is equal to  
where  <math>\nu_{0}</math> is a base value approximately equal to the kinematic viscosity, <math>c_0</math> is an empirical coefficient, <math>c_{sm}</math>  is an empirical coefficient (Smagorinsky coefficient), <math> \Delta </math> is the local cell area, and <math>|S|</math> is equal to  


       <math> |S| = \sqrt{2 \biggl( \frac{ \partial U}{\partial x} \biggr) ^2 +  2 \biggl( \frac{ \partial V}{\partial y} \biggr) ^2 + \biggl( \frac{ \partial U}{\partial y} + \frac{ \partial V}{\partial x}  \biggr) ^2 } </math>
       <math> |S| = \sqrt{ \biggl( \frac{ \partial U}{\partial x} \biggr) ^2 +  \biggl( \frac{ \partial V}{\partial y} \biggr) ^2 + \frac{1}{2} \biggl( \frac{ \partial U}{\partial y} + \frac{ \partial V}{\partial x}  \biggr) ^2 } </math>





Revision as of 04:36, 1 February 2010

Subgrid Turbulence Model

In CMS-Flow eddy viscosity is calculated as

       

where is weighting factor equal to in which is the significant wave height and and are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of Kraus and Larson (1991)

     

where is an empirical coefficient (default is 0.5), and is the wave bottom orbital velocity and is the water depth. The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress

     

where is a base value approximately equal to the kinematic viscosity, is an empirical coefficient, is an empirical coefficient (Smagorinsky coefficient), is the local cell area, and is equal to

     



References

LARSON, M.; HANSON, H., and KRAUS, N. C., 2003. Numerical modeling of beach topography change. Advances in Coastal Modeling, V.C. Lakhan (eds.), Elsevier Oceanography Series, 67, Amsterdam, The Netherlands, 337-365.


CMS-Flow