Commit c75ea8e8 authored by Kilian Lackhove's avatar Kilian Lackhove
Browse files

APE: adjust userguide to formulation change

parent b439d56b
......@@ -14,16 +14,16 @@ irrotational acoustic perturbations, in this case perturbations are assumed to
be exclusively of acoustic nature.
\begin{subequations}
\begin{align*}
\frac{\partial p'}{\partial t}
+ \overline{c}^2 \frac{\partial \overline{\rho} u'_i}{\partial x_i}
+ \overline{c}^2 \frac{\partial \overline{u}_i p' / \overline{c}^2}{\partial x_i}
&= \overline{c}^2 q_c
\\
\frac{\partial u'_i}{\partial t}
+ \frac{\partial \overline{u}_j u'_j}{\partial x_i}
+ \frac{\partial p' / \overline{\rho}}{\partial x_i}
&= 0
\end{align*}
\frac{\partial p'}{\partial t}
+ \frac{\partial \gamma \overline{p} u'_i}{\partial x_i}
+ \frac{\partial \overline{u}_i p'}{\partial x_i}
&= \overline{c}^2 q_c
\\
\frac{\partial u'_i}{\partial t}
+ \frac{\partial \overline{u}_j u'_j}{\partial x_i}
+ \frac{\partial p' / \overline{\rho}}{\partial x_i}
&= U_i
\end{align*}
\end{subequations}
where $(\overline{u}_i,\overline{p}, \overline{\rho}, \overline{c}^2 = \gamma \overline{p} / \overline{\rho} )$ represents the base flow and $(u'_i,p')$ the perturbations.
$\overline{c}^2 q_c$ is the acoustic source term.
......
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