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I am trying to simulate a moving airfoil with constant speed (Mach=0.755, aoa=1.25). I solve Euler equations with Roe's method. I have two boundary conditions:

  1. Farfield
  2. Slip wall (airfoil)

For all faces I gave face velocities as:

vbx = -Mach cos (aoa)

vby = -Mach sin (aoa)

At the farfield, I set

(rho,u,v,p) = (1, 0, 0, 1/gamma)

where gamma is the ratio of specific heats.

For slip wall I set velocity as the tangential velocity of the neighbor near boundary cell.

The flow is initialized with zero (u,v) everywhere. But with these boundary conditions residual is zero so there is no point to iterate. Residual is the summation of fluxes where flux is defined as:

Fn0 = rho*(un-vb)

Fn1 = rho*(un-vb)*u + p*nx

Fn2 = rho*(un-vb)*v + p*ny

Fn3 = E*(un-vb) + p*un

So how should be the proper boundary conditions?

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I found the problem. I forgot to add face velocity when updating the airfoil surface. It should be:

u = tangX + vbx
v = tangY + vby

where, tangX and tangY are the x and y components of the tangential velocity of the neighbour interior cell. Then, the flux at the airfoil surface should be:

Fn0 = 0;
Fn1 = p*nx;
Fn2 = p*ny;
Fn3 = un * p;

Note that, un is not zero due to face velocity but (un-vb) is zero.

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