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I understand that you must reflect the velocity of the cell across the wall and store that reflected velocity in the ghost cell (which will then be used for flux/residual calculations), but that is the extent of my understanding. I have tried implementing this in my euler flow solver but I am still seeming to get issues which makes me think there must be more to implementing a wall boundary condition.

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  • $\begingroup$ I guess a wall means here that there is no flow through this boundary. Then the BC must enforce zero flow velocity normal to the boundary. $\endgroup$ May 3 at 23:52
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Specifying velocity boundary conditions isn't enough. If you are indeed solving the 2D Euler equations, you will also need to specify boundary conditions for density and temperature (if you are using primitive variables which I assume you are).
Maxim is correct that you need to enforce zero velocity normal to the wall in addition to the no slip condition. For the mass denisty equation, you could use $\rho_{ghost} = \rho_0$ where 0 is the index of the interior cell on the wall boundary.
The wall BC for the energy equation needs a little more information. Is your wall adiabatic? If so, the ghost cell implentation is similar to the one above for the mass density. Furthermore, you could choose the value of the temperature in the ghost cell to represent a prescribed heat flux through the wall. If the temperature of the wall is to be prescribed by the user, then:
$$T_{ghost}=2T_w -T_0$$
This is all valid if you are using one layer of ghost cells, but can easily be extended to multiple layers for higher order solvers.

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