Boundedness Property
 

Hi Dear Friends.

I am have seen in the CFD literature the term BOUNDEDNESS PROPERTY. Could someone explain.

Thanks

VGF

Re: Boundedness Property
 

As far as I know, the boundness comes from treating the convection terms. If you use the higher order schemes such as the QUICK scheme, the scheme results in undershoots or overshoots which are physically incorrect and may result in stablity problem. The bounded scheme remedies such a problem. The purpose of bounded scheme is to get an accurate solution like the higher order schemes while preserving the boundedness of problem. See the paper "Curvature-Compensated Convective Transport; SMART, a New Boundedness Preserving Transport Algorithm, by Gaskell, P. H. and Lau, A. K. C., International Journal of Numerical Methods in Fluids,Vol.8, pp 617-641, 1988.

Re: Boundedness Property
 

When one solves for the mixture fraction (MF) (which is usually bounded between 0 and 1), using schemes such as central difference results in scalar values that are below 0 and above 1. To correct this, normally such out of bound values are clipped to the limit. So if MF>1 then force MF=1 and if MF<0 force MF=0. It is desirable to have a numerical scheme that automatically preserve bounds. The Quick scheme uses a high-order upwind interpolation and is better than the central difference scheme when it comes to maintaining MF boundedness. However it is also not sufficient. There may be papers out there that address such issues. One such can be found here:

http://ctr.stanford.edu/ResBriefs04/herrmann2.pdf

according to Versteeg and Malalasekra's book, boundness means that
1. all properties should be bounded by its own boundary values.
e.g. for pure convection problem, if the maximum and minimum T is 200 and 100, then when you do CFD, all the T value on the field should between 100 and 200(no overshoot/undershoot)
2. all coefficients of the discretized equations should have the same sign
e.g. if T on one cell increase, then the neighbour cells' T should also increased.