[fjavi90]

Hello everybody,

A very common approach for WENO schemes when imposing slip boundary condition for the Euler equations is using ghost points. To do that the wall is located on an interface midway between nodes of the mesh and the ghost points values are mirrored from that of the interior points (except for the normal velocity to the wall which is negated). It is the technique employed in the original paper by Jiang and Shu.

o----o----o----|----o----o----o
G3--G2--G1--|----1----2----3

Following the sketch above,
density(G1) = density(1)
density(G2) = density(2)
density(G3) = density(3)
and so on...

This approach is conservative.

I am employing a Finite Difference WENO 5 with Lax-Friedrichs flux splitting.
Is there a similar way to locate the wall in a mesh node instead of in an interface?

o----o----o---x----o----o----o
G3--G2--G1--w----1----2----3

I have tried the same philosophy: mirroring the interior values onto the ghost points, imposing that the normal component of the velocity at the wall (labeled as w, which is now a mesh node) should be zero, and extrapolating the density and pressure from the neighbouring node.

This second approach however does not seem to be conservative, because although it works fine for low-mach cases, it produces unphysical shock behaviour when trying to model supersonic cases.

Is there something I am missing?

Thanks in advance.

[praveen]

If your grid point is on the wall, then half of your cell is outside the domain. I dont see how to satisfy conservation in this case. Also imposing slip bc seems difficult since we usually incorporate this into the fluxes, but there are no boundary fluxes if your cell cuts the boundary.

You can of course do FD WENO but have your grid points off the boundary. Then you will have a cell face exactly on the boundary.