The meaning of 'dTdtCross' term in the output of Ember?

[Marques]

Dear colleagues,

I'm recently simulating an oxygen-Enriched air/ methane counterflow diffusion flame using Ember, and confused by the term 'dTdtCross' in its output. It is easy to understand the meanings of 'dTdtProd' or 'dTdtDiff'. I have retrieved this term in Docs saying 'dTdt due to gradients in species composition'. But could anyone tell me the exact meaning of ''dTdtCross'', and what is 'gradients in species composition'?  

Thank you!

Regards,

Marques

[Ray Speth]

Hi Marques,

"dTdtCross" includes the term in the energy equation as shown here (the very last equation) that is a summation of the diffusive fluxes (j_k) times the temperature gradient. These "cross" terms, which couple multiple solution components at different grid points, are treated as constants during each operator-split time step so that the other terms (convection / diffusion / production) can be integrated in parallel at different grid points or for different solution components.

Regards,

Ray