non reflecting boundary condition?
what is meant by non reflecting boundary condition? what are the conditions under which we need to apply this condition? i know that under the conditions of compressible subsonic duct flows , the pressure waves affect the solutions by reflection under transient responses. are there any more situtaions?
Re: non reflecting boundary condition?
non-reflective boundary conditions means exactly what it means, that the conditions are imposed at the boundary in such a way that no disturbance (waves and other) will be reflected, they will cross the boundary and exit the computational grid without any trouble. Here what I am talking about is for time dependent problems; I never dealt with steady state problems so I am not sure how this will affect the flow in that case, but I am sure it will.
If you ask me, I would suggest anybody to use non-reflective boundary conditions whenever there is an 'open' boundary (not a rigid wall). And this is because, even if waves don't seem to be reflected at the boundary, they actually are. As a consequence you might trap waves in your computational domain and have artificial resonances.
When the viscosity is high and the flow is subsonic, the reflected waves at the boundary have low amplitude and are damped quickly, this is why many people do actually neglect the treament of non-reflective boundary conditions in such cases.
However, when viscosity is low and the Mach number in the flow is large (approaches 1), then the reflected waves are noticed and can affect substancially the results and easily lead to divergence of the numerical scheme.
When working with high order methods (such as Spectral Methods), one has always to treat the boundaries with extreme care and non-reflective boundary conditions must be imposed (on the characteristics of the flow) at the open boundaries otherwise the numerical scheme is 'explosive' and diverges within a few time steps!
See for example:
Givoli, 1991, J. Comput. PHys, vol. 94, page 1.
Abarbanel, Don, Gottlieb, Rudy and Townsend, 1991, J. Fluid Mech., vol. 225, page 557.
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