Hi all !

I'm a PhD student, and I'm writing a code for the stability study of the flow inside a leading-edge slat cavity.

I use the incompressible Euler equations. They are elliptic. Conquequently, I have a big issue for the choice of the bounday conditions, especially at the entry of the cavity, where the flow has no special properties.

I cannot use the method of characteristics because of the ellipticity of the equations. So, well, I'm a bit lost, and some advices will be helpfull !

Thanks !

Unfortunately, I can't give you an answer. But one question: why using Euler's equations ? Navier-Stokes is a much better model, and MUCH more numerically stable.

I would advice making a N-S solver with high viscosities, and then decreasing the viscosity if the convergence can be achieved.

> But one question: why using Euler's equations ?

First, it's was a choice made a long time ago, and since I am in my third year thesis, I don't have enough time to make a N-S solver. But that would be a potential involvement for further works.

> Navier-Stokes is a much better model

It depends on the physical problem you are considering. In my case, viscosity on not of critical interest, and the stability method I am developping would be much more complicated with order 2 derivatives.

> and MUCH more numerically stable.

I am using a spectral collocation method, wich in very very numerically stable

I think, I will use an extrapolation condition in a first attempt. Does anyone have an opinion on that ?

Is it meaningfull to consider the flow to be locally compressible near the boundary ? Then, the system would be hyperbolic near the boundary and i could use classical nonreflecting boundary conditions.

Am I right ?