B.C. by Poinsot and Lele
 

I implemented the boundary conditions described in the article "boundary conditions for direct simulations of compressible viscous flow" by Poinsot and Lele (journal of comp. physics 101, 104-129 (1992)). However I run into stability problems when using the slip-wall boundary condition. Does anybody has experience with these bc? Any help is welcome.

Greetings,

Jan Ramboer

Re: B.C. by Poinsot and Lele
 

Hi Jan,

a guess: the boundary conditions for viscous flows are probably to treat a non-slip condition at the boundary with the development of a boundary layer there. THerefore, your slip-wall boundary condition might be in contradiction with some basic assumptions in the method. I do not have at the moment access to the paper you mentioned, so this is only a guess.

I do work with compressible viscous time-dependent flow problems and I do implement the boundary conditions using the method of characteristics, which makes sure that waves (and numerical instabilities) are not reflected back into the computational domain from the boundaries.

Cheers,

Patrick

Re: B.C. by Poinsot and Lele
 

Are you using your own formulation or is this the same one as described in the article i mentioned?

Greetings,

Jan

Re: B.C. by Poinsot and Lele
 

I think the non-reflecting boundary conditions (method of characteristics) is hyperbolic as the boundary layer is parabolic. Thus you would need to start with no boundary layer at all, I would say. Or is this totally wrong?

Re: B.C. by Poinsot and Lele
 

The Methods of characteristics is usually used for open boundaries, but can (I would say 'partially') be used for rigid boundary, and especially in a case where a slip condition is applied (which means that the tangential velocity is not zero).

When you have an open boundary then the effect of the viscosity is negligible there and one can treat a viscous flow at an open boundary using the method of characteristics, which is basically a treatment for inviscid problem (but this work since the effect of the viscosity is negelcted).

At a wall, with a non-slip boundary condition, a boundary layer develops there due to the viscous effects. However, if you have a slip-condition there, then there is no boundary layer of the tangential flow, and in that sens the tangential flow does not 'feel' the wall (like an inviscid flow).

Patrick

Re: B.C. by Poinsot and Lele
 

As I wrote you, I do not have access to this paper and therefore I have no clue what treatment is given there, but only a guess.

THe method of characteristics is usually for open boundaries, however a slip condition is in some sens similar to an open boundary.

What are your boundaries? Open boundaries? or rigid walls? What is the approach in the paper of Poinsot and Lele?

The methods of characteristics is a well known method to treat flows at open boundaries. THere are many ways of applying it and many other approaches for non-reflective (open) boundaries.

Cheers,

Patrick

Hello Patrick,
I have read your post about the method of characteristics.
Could you please tell me some papers working on it?
I´m working in a wave tank simulation and trying to avoid reflections

Cheers

Mar.

well, this is a 10 years old discussion that you are resuscitating...

I am not sure what journals you have access to but here are a few references.

Gottlieb, D., Gunzburger, M., Turkel, E., 1982, SIAM J. Numer. Anal., n.19, p. 671 (On numerical boundary treatment for hyperbolic systems)

Abarbanel, S., Don, W.S., Gottlieb, D., Rudy, D.H., Towsend, J.C., 1991, Journal of FLuid Mechanics, n.225, p.557 (Secondary frequencies in the wake of a circular cylinder with vortex shedding - that paper shows how wrong boundary conditions induces additional frequencies and how to apply BC correctly).

Wasberg, C.E., Andreassen, O (O with a bar!), Computer Methods in Applied Mechanics and Engrg., 1990, n. 80, page 459 (this show a treatment of boundary conditions for Spectral Methods which can can actually be applied to other methods).

There is also an old review paper (which was brand new when I was doing my PhD...), by Dan Givoli:
Givoli, D., 1991, Journal of Computational Physics, n. 94, page 1.

and if you want you can try one of my old papers... have a look at the treatment of the boundary conditions.

http://articles.adsabs.harvard.edu/c...;filetype=.pdf

though there is a typo in equation 18 (i) [it should be rho_0 + delta rho instead of rho_0 delta rho ]