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

$$% \begin{align*}%\label{shock:IC} \rho_L = 1, u_L = M_L \gamma^{1/2}, p_L = 1,\quad \rho_R = \rho_L K_1, u_R = u_L K_1^{-1}, p_R = p_1 K_2,$$

where

$$% \begin{align*}%\label{shock:IC1} K_1 = \frac{\gamma+1}{2} \frac... ...\quad K_2 = \frac{2}{\gamma+1}\left(\gamma M_L^2 - \frac{\gamma- 1}{2}\right).$$

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

$$\begin{displaymath}<tex2html_comment_mark>7 c_1 = u_c/ r_c, c_... ...{-2}/2,\quad r = ((x_1-0.5)^2 - (x_2 - 1)^2)^{1/2}, \nonumber \end{displaymath}$$

where we set $r_c =0.075$ and $u_c= 0.5$. The computations are stopped at the dimensionless time $T=0.7$.