CMS-Flow:Subgrid Turbulence Model: Difference between revisions

From CIRPwiki
Jump to navigation Jump to search
Line 3: Line 3:


The eddy viscosity is calculated as <math> \nu_t = (1-\theta_m)\nu_{tc} + \theta_m \nu_m </math>  where <math>\theta_m</math>  is weighting factor equal to <math>\theta_m = (H_s/h)^3 </math>  in which <math>H_s</math>  is the significant wave height and <math>\nu_{tc}</math>  and <math>\nu_{tw}</math>  are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of KRAUS and LARSON (1991)  <math> \nu_tw = \Lambda u_w h </math>, where  <math>del</math> is an empirical coefficient (set to 0.5 here), and  <math>u_w</math> is the wave bottom orbital velocity. The current-related eddy viscosity is calculated using a subgrid turbulence in which the turbulent eddy viscosity is a function of the flow gradients and the grid size model of the form  
The eddy viscosity is calculated as <math> \nu_t = (1-\theta_m)\nu_{tc} + \theta_m \nu_m </math>  where <math>\theta_m</math>  is weighting factor equal to <math>\theta_m = (H_s/h)^3 </math>  in which <math>H_s</math>  is the significant wave height and <math>\nu_{tc}</math>  and <math>\nu_{tw}</math>  are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of KRAUS and LARSON (1991)  <math> \nu_tw = \Lambda u_w h </math>, where  <math>del</math> is an empirical coefficient (set to 0.5 here), and  <math>u_w</math> is the wave bottom orbital velocity. The current-related eddy viscosity is calculated using a subgrid turbulence in which the turbulent eddy viscosity is a function of the flow gradients and the grid size model of the form  
       <math> \nu_{tc} = \nu_{t0} + \sqrt{ (c_0 u_{*} h)^2 + (l_h^2 \abs{S} )^2 } </math>
       <math> \nu_{tc} = \nu_{t0} + \sqrt{ (c_0 u_{*} h)^2 + (l_h^2 |S|} )^2 } </math>


where  <math>\nu_{t0}</math> is a base value approximately equal to the dynamic viscosity, and <math>c_0</math>  is an empirical coefficient and  <math>l_h</math> is the subgrid mixing length. The mixing length is calculated here as  <math>l_h = \kappa min( \sqrt{\delta x \delta y}, c_{sm} h) </math> where <math>c_{sm}</math>  is an empirical coefficient (Smagorinsky coefficient).
where  <math>\nu_{t0}</math> is a base value approximately equal to the dynamic viscosity, and <math>c_0</math>  is an empirical coefficient and  <math>l_h</math> is the subgrid mixing length. The mixing length is calculated here as  <math>l_h = \kappa min( \sqrt{\delta x \delta y}, c_{sm} h) </math> where <math>c_{sm}</math>  is an empirical coefficient (Smagorinsky coefficient).

Revision as of 23:10, 23 October 2009

Subgrid Turbulence Model

The 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 (set to 0.5 here), and is the wave bottom orbital velocity. The current-related eddy viscosity is calculated using a subgrid turbulence in which the turbulent eddy viscosity is a function of the flow gradients and the grid size model of the form

     Failed to parse (syntax error): {\displaystyle  \nu_{tc} = \nu_{t0} + \sqrt{ (c_0 u_{*} h)^2 + (l_h^2 |S|} )^2 } }

where is a base value approximately equal to the dynamic viscosity, and is an empirical coefficient and is the subgrid mixing length. The mixing length is calculated here as where is an empirical coefficient (Smagorinsky coefficient).