Computational Fluid Dynamics -I (CFD-I) Session #13
FINITE VOLUME METHOD FOR CONVECTION-DIFFUSION PROBLEM (part II)
convection term FINITE VOLUME METHOD FOR CONVECTION-DIFFUSION PROBLEM
FINITE VOLUME METHOD
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What are the difference between convection and diffusion from CFD point of view?!
the diffusion process affects the distribution of a transported quantity along its gradients in all directions, whereas convection spreads influence only in the flow direction.
ΦC 8/3). This gives rise to stability problems and unbounded solutions under certain flow conditions.
the discretised equations involve not only immediate-neighbour nodes but also nodes further away. 26
Tri-diagonal matrix solution methods are not directly applicable
The QUICK scheme can give (minor) undershoots and overshoots 27
TVD (total variation diminishing) schemes As discussed earlier, the basic upwind differencing scheme is the most stable and unconditionally bounded scheme, but it introduces a high level of false diffusion due to its low order of accuracy (first-order). Higher-order schemes such as central differencing and QUICK can give spurious oscillations or ‘wiggles’ when the Peclet number is high. wiggles can give physically unrealistic negative valuesand instability.
TVD schemes are designed to address this undesirable oscillatory behavior of higher-order schemes. In TVD schemes the tendency towards oscillation is counteracted by adding an artificial diffusion fragment or by adding a weighting towards upstream contribution. In the literature early schemes based on these ideas were called flux corrected transport (FCT) schemes 28
CFD
End of Session #13 Next Session :
Thanks Dr. Mohammad Jadidi (Ph.D. in Mechanical Engineering)
[email protected]
https://ir.linkedin.com/in/moammad-jadidi-03ab8399 https://www.researchgate.net/profile/Mohammad_Jadidi https://www.slideshare.net/MohammadJadidi
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