Sometimes we hear somethings on stiffness problem of solution for chemical reaction modeling.
https://en.wikipedia.org/wiki/Stiff_equation
There is an option in Fluent software to figure it out.
http://www.afs.enea.it/project/neptunius/docs/fluent/html/th/node348.htm
Have you guys used it so far? tell us when and why did you use it?
Hi Roh,
stiff equations may occur when you want to solve sets of kinetic equations exhibiting very different speeds (typically, with k0 values spanning over 8-10 orders of magnitude, or more).
This may happen when you are modelling processes involving molecular (rather slow) and radical (extremely fast) phenomena. The stiffness is enhanced if you are opting for a detailed spatial description, as in CFD studies. In my case, I had to deal with stiffness when modelling ozonation processes, see chapter 2 of my PhD thesis:
Thesis Modelling Ozonation Processes for Disinfection By-Product Co...
Hope it helps,
Pierre
As Pierre Mandel kindly mentioned, when characteristic scales of your problem are very far (orders of magnitude) you see Stiff Differential Equations (ODE or PDE), It means you have small stability region or it means you have second or third order "Bifurcation" which needs a very high order numerical solution schemes and small time (discretization in general) steps.
There are two types of stiff problems in modeling advection-diffusion-reaction (ADR):
- If you model single specie, when time scale of Peclet number and Damkohler number are very different, you have an stiff ADE (or ADR, or transport equation), you can solve it either by implicit solver or small time steps, or dual time step, or other numerical tricks.
- If you have multi-rate mass transport and your species are internally related (reactive transport), you cannot solve this problem with small time step. Mathematically you have to get integral of infinity and you are always unstable. Those problem can only be solved with implicit solvers (all species in one shot!)
If you need more information on this topic, a very good and classic source for learning is this book chapter:
Approaches to modeling of reactive transport in porous media
Carl I Steefel, Kerry TB MacQuarrie Publication date: 1996/1/1 Reviews in Mineralogy and Geochemistry Volume 34 Issue 1 Pages 85-129 Publisher GeoScienceWorld
Dear Roh,
I am working on non-premixed flames, and i have used stiff equation option in fluent to solve the divergence problem.
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