# Euler Equations Boundary Conditions

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April 5, 2013, 13:51
Euler Equations Boundary Conditions
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Dear CFD Community,

I'm currently trying to fix a problem with my subsonic boundary condtions for the 2d Euler equations. Attached you can see a contour plot of my problem. The problem can be found in

" A. LERAT, C. CORRE. A residual-based compact scheme for the compressible Navier-Stokes equations. Journal of Computational Physics, 170, p. 642-675, 2001. "

I'm using a two step Lax Wendroff scheme with a third smoothing step and the solver is vertex centered=> the boundary match with the physical boundary. Moreover there are fictitious cells around my boundary. My problem is the high entropy production on the lower side after the bump, the too small peak Mach number (Lerat has 0.95) and the deviation at the inlet. The walls are modelled by using fictitious cells where the velocity of the first interior line is mirror-sided and thus enforcing zero mass flux.

For the supersonic case everything is alright but for this case I'm suspecting my boundary condtions for the deviation. The reference is set to freestream and e.g. u8=1 and rho8=1. Based on the freestream Mach number M8 I can get all freestream variabels.

I prescribe the incoming Riemann Invariant R+= 1 + 2/(M8*(gamma-1)) and the entropy s8=1 at the inlet and extrapolate R- from the interior. Based on that I get my actual speed of sound a and the normal velocity.

For the outlet I do it similarly where I extrapolate s and R+ and prescribe the pressure (here freestream pressure p8). This gives me the density by using the entropy relation and so the speed of sound.

I do all of this exactly on the boundary since my second lines (2:i_max-1 & 2:j_max-1) define my boundary and all sourrounding fictitious points are just updated by linear extrapolation except for the fictitious wall points.

What might I do wrongly here?

Thank you very much

P.S. In the plot upper and lower are changed.

Christian
Attached Images
 contour.jpg (18.7 KB, 13 views) plot.jpg (30.5 KB, 13 views)

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