1.3.1 Hydrodynamics equations including viscosity

The viscous hydrodynamics equations are

$\begin{displaymath} { \!\! \renewedcommand{arraystretch}{2.0} \begin{array}... ...dmath$\scriptscriptstyle v$}}} \right) & = & 0 \end{array}} \end{displaymath}$

(21)

with the stress tensor $\bgroup\color{HIGH1color}$\bar{\bar{\ensuremath{\mathsf{T}}}}$\egroup$ (including a term for the gas pressure)

$\begin{displaymath} \bar{\bar{\ensuremath{\mathsf{T}}}} = - P \bar{\bar{\ensu... ...ptstyle v$}}} \bar{\bar{\ensuremath{\mathsf{I}}}} \right\} \end{displaymath}$

(22)

depending on the dynamic viscosity $\bgroup\color{HIGH1color}$\mu$\egroup$ .

Note: via $\bgroup\color{HIGH1color}$\bar{\bar{\ensuremath{\mathsf{T}}}}$\egroup$ Eq. (21) contains second derivatives.