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How to define blending factor?

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Old   June 4, 2003, 04:23
Default How to define blending factor?
Julie Polyakh
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Does anybody know how to define blending factor for discretization schemes?

The case I deal with includes turbulent flow with combustion and conjugate heat transfer.


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Old   June 4, 2003, 06:14
Default Re: How to define blending factor?
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Blending factor is defined as being the amount of higher-differencing scheme (hence MARS,SCFD,CD,etc...) you take relatively to the first-order discretisation scheme (UD). For example, if you have a blending factor of MARS 0.8, the space derivatives are calculated by using a first order scheme weighted by 0.2 and a using the MARS discretisation scheme weighted by a factor of 0.8. In fact, it is a little bit more complicated than that, but if you have some spare time, take a look to the book Computational Methods for Fluid Dynamics, Ferziger & Peric, Springer, 2002. Take a closer look at the section dealing with deferred correction and discretisation of convective fluxes.
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Old   June 4, 2003, 07:46
Default Re: How to define blending factor?
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The so called blended differencing schemes are CD, LUD, and QUICK in Star-CD.

MARS is different ! In MARS the blending factor is NOT a factor defining blending between a first order scheme and a second order scheme as it is in the other schemes but it is more a compressibility factor that defines how well it captures sharp discontimuities in the solution. MARS is a TVD-based scheme and many different TVD-schemes can be obtained by only varying how well does it capture discontinuities. Note also that MARS is always formally second order accurate, no matter what is the bf used.

In case you use bf=1.0 for MARS it captures as well as possible discontinuities BUT be aware that it can also lead to unphysical behavior. Without an additional entropy condition (which is most likely not in Star) this can lead to a situation were the solution is actually making sharp discontinuities, e.g. like high velocity or temperature peaks.

My advise is that with MARS use bf=0.5 at the most. This usually gives good solutions. With academic cases you may be able to use bf=1.0 with MARS.
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