From 30e36d2f5a7543b11196c2b836e0e6c41e5f223c Mon Sep 17 00:00:00 2001 From: bangerth Date: Fri, 30 Sep 2011 17:27:23 +0000 Subject: [PATCH] Fix a couple of formulas. git-svn-id: https://svn.dealii.org/trunk@24490 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-32/doc/intro.dox | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/deal.II/examples/step-32/doc/intro.dox b/deal.II/examples/step-32/doc/intro.dox index b0b2e95195..7e1e732679 100644 --- a/deal.II/examples/step-32/doc/intro.dox +++ b/deal.II/examples/step-32/doc/intro.dox @@ -436,12 +436,12 @@ has been shown to work well for the given case, $\alpha = 1$ in step-31, but it is usually less effective as the diffusion for $\alpha=2$. For that case, we choose a slightly more readable definition of the viscosity, @f{eqnarray*} - \nu_2(T)|_K = \min (\nu_h^\mathrm{max}|_K,\nu_h^\mathrm{E}_K) + \nu_2(T)|_K = \min (\nu_h^\mathrm{max}|_K,\nu_h^\mathrm{E}|_K) @f} where the first term gives again the maximum dissipation (similarly to a first order upwind scheme), @f{eqnarray*} - \nu^\mathrm{max}_h|_K = \beta h_K \|\ve u\|_{L^\infty}(K)} + \nu^\mathrm{max}_h|_K = \beta h_K \|\mathrm u\|_{L^\infty}(K)} @f} and the entropy viscosity is defined as @f{eqnarray*} @@ -457,7 +457,7 @@ with $T_m$ an average temperature (we choose the mean between the maximum and minimum temperature in the computation), which gives the following formula @f{eqnarray*} R_\mathrm{E}(T) = \frac{\partial E(T)}{\partial t} + - (T-T_\mathrm{m}) \left(\ve u \cdot \nabla T - \kappa \nabla^2 T - \gamma\right). + (T-T_\mathrm{m}) \left(\mathrm u \cdot \nabla T - \kappa \nabla^2 T - \gamma\right). @f} The denominator in the formula for $\nu^\mathrm{E}_h|_K$ is computed as the global deviation of the entropy from the space-averaged entropy $\bar{E}(T) = -- 2.39.5