Changes between Version 9 and Version 10 of doc/tec/sgs

Timestamp:

Jul 20, 2018 1:53:19 PM (6 years ago)

Author:

gronemeier

Comment:

--

doc/tec/sgs

@@ -97 +97 @@
 == Dynamic subgrid-scale model ==
 
-The dynamic SGS model, based on an idea of [#germano Germano et al. (1991)], can be used as an alternative to the Moeng-Wyngaard version of the Deardorff model. In this case, ''K'',,m,, is calculated as
+The dynamic SGS model can be used as an alternative to the Moeng-Wyngaard version of the Deardorff model. In this case, ''K'',,m,, is calculated as
 {{{
 #!Latex
@@ -137 +137 @@
 #!Latex
 \begin{align*}
-   \overline{S}_{ij} = \frac{1}{2}\left(\frac{\partial\overline{u_i}}{\partial x_j} + \frac{\partial\overline{u_j}}{\partial x_i} \right)
+   \overline{S}_{ij} = \frac{1}{2}\left(\frac{\partial\overline{u_i}}{\partial x_j} + \frac{\partial\overline{u_j}}{\partial x_i} \right) \quad \mathrm{and} \quad \overline{S}^d_{ij} = \overline{S}_{ij} - \frac{1}{3}\overline{S}_{kk}\delta_{i,j}
 \end{align*}
 }}}
-the strain tensor and ''ν,,t,,'' the SGS viscosity. Unlike other dynamic models this formulation of ''c'',,*,, is not derived using model assumptions for the subgrid stress and the stress on the test filter level, but is based on proven turbulence properties ([#heinz2008 Heinz, 2008]; [#heinz2012 Heinz and Gopalan, 2012]). Furthermore, the stability of the simulation is ensured by using dynamic bounds that keep the values of ''c'',,*,, in the range
+the strain tensor and the deviatoric strain tensor, repsectively, and ''ν,,t,,'' the SGS viscosity. Unlike other dynamic models this formulation of ''c'',,*,, is not derived using model assumptions for the subgrid stress and the stress on the test filter level, but is based on proven turbulence properties ([#heinz2008 Heinz, 2008]; [#heinz2012 Heinz and Gopalan, 2012]). Furthermore, the stability of the simulation is ensured by using dynamic bounds that keep the values of ''c'',,*,, in the range
 {{{
 #!Latex