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The computational domain is $\Omega = (0,2)\times(0,2)$ with the periodic extension
in the $x_2$-direction.
A stationary plane shock wave is located at $x_1= 1$. The prescribed pressure
jump through the shock is $p_R - p_L =0.4$, where $p_L$ and 
$p_R$ are the pressure values
from the left and  right of the shock wave, respectively, corresponding to  
the inlet (left) Mach number $M_L = 1.1588$. 
The reference density and velocity are those of the free uniform flow
at infinity. 
In particular, we define the initial density, $x_1$-component of velocity and pressure by
$$% \begin{align*}%\label{shock:IC}
  \rho_L = 1,\ u_L = M_L \gamma^{1/2},\ p_L = 1,\quad
  \rho_R = \rho_L K_1,\ u_R = u_L K_1^{-1},\ p_R = p_1 K_2,
$$%\end{align*}
where
$$% \begin{align*}%\label{shock:IC1}
K_1 = \frac{\gamma+1}{2} \frac{M_L^2}{1+ \frac{\gamma-1}{2}M_L^2},\quad
K_2 = \frac{2}{\gamma+1}\left(\gamma M_L^2 - \frac{\gamma- 1}{2}\right).
$$%\end{align*}
Here, the subscripts $_L$  and $_R$ denote the quantities at $x < 1$ and $x>1$, respectively,
$\gamma=1.4$ is the Poisson constant.
The Reynolds number is 2000.
An isolated isentropic vortex centered at $(0.5, 1)$  is added to the basic flow.
The angular
velocity in the vortex is given by
\begin{align*}
$$%v_{\theta} = c_1 r \exp(-c_2 r^2),\quad 
c_1 = u_c/ r_c,\ \ c_2 = r_c^{-2}/2,\quad 
r = ((x_1-0.5)^2 - (x_2 - 1)^2)^{1/2}, \nonumber
$$&\end{align*}
where we set $r_c =0.075$ and $u_c= 0.5$. 
The computations are stopped at the dimensionless time $T=0.7$.

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