Can SIMPLE or SIMPLER be used to solve a transient, bouyancy driven flow ? If yes, How ? What other methods can be used ?

Thanks

Ravi

Hi,

Yes, you can catch a transient behaviour in a buoyancy-driven flow. But you have to use a small time step, e.g. keep the CFL number less than about 0.3. You can have a look at one of Katta's papers, among others:

V. R. Katta and L. P. Goss and W. M. Roquemore,"Effect of nonunity Lewis number and finite-rate chemistry on the dynamics of a hydrogen-air jet diffusion flame ", Combustion and Flame, vol. 96, pp.60-74 (1994)

The best way is to use DNS or LES.

best regards,

Xu

SIMPLE(R) is only the way to handle pressure for a set of incompressible NS equations. Recall that it stands for semi-implicit pressure linked equations. So, it has little to do with the discretization of PDEs into algebraic set of equations. Cfd-people imply that SIMPLE should be used only with the finite (control) volume methods, as it has been outlined in S.V.Patankar's book "Numerical Heat and Mass Transfer (?)" -- the "bible" for cfd beginners. For that reason many cfd'ers believe SIMPLE=F(C)VM. Not exactly! It is possible to extend SIMPLE to other methods, finite elements, boundary elements. Though, it may not be the best to couple advanced methods with SIMPLE. Nevertheless, it has been done in literature, maybe, mainly to say, "Oh, well, I did it...".

Coming back to your question, of course, SIPMLE(R) may be used for transient buoyancy driven flows. Problem is accuracy. On the first hand, SIPMLE becomes very inaccurate for bouyancy forces dominate over convection forces due to the way you link pressure with the NS equations. Next, it mostly depends upon the discretization scheme used for the PDEs. This is the most crucial moment. COBOK