I wanted to know as to what can be used as a convergence criteria for a three dimensional jet in crossflow type of problems. The flow field is dominated by vortical and shock structures. Also some generic references to convergence studies for three dimensional compressible flow fields will be of great help amol

Amol,

To start with, there is quite a large body of literature on this subject, including experimental, which you may compare to. I studied this subject more than 10 years ago, and compared to papers of Spaid (AIAA J, 13(11), 1430-4, 1975), Shang et al (AIAA J, 27(3), 323-9, 1989) and Brandeis (ICAS-92-4.9.1 paper, ICAS conf. 1992, Beijin).

To answer your question: There are few convergence tests you should consider.

First, in a specific run, you should verify that the residuals of all the transport equations you solve reduce to a small fraction of a characteristic value of each eqauation (e.g., for the continuity equation the residual should reduce to a small fraction of the total mass flowrate entering the domain, and in complete analogy, the same applies to the enregy equation etc.).

Another convergence test you need to pass is the grid independency (including time steps for transient simulation). By systematic grid refinement and result comparison on the various grid levels you should see how much quantities of interest in the simulation (e.g., shock wave location and temperature jump across them in your case) are close to grid independence.

I hope this helps, Rami

A converged solution is specific for the used mesh ... thats why the grid independency is not part of this.

Much more important is, that the values in the flow field and especially the integral values like heat flux, torque, lift and drag do not change any more (for steady state) or are periodic (transient with steady b.c.)

Thanks a lot Rami and Jorn.

I think suggesations of both of you are important to what I am looking. My final objective is to achieve grid independence. So in case I have G grid refinements then I would need to be sure that the result for each grid (1,2,..G) is converged.

Most of previous numerical work used surface pressure and temperature on the wall as the convergence criteria but I am not sure wether such convergence test would imply that a strict convergence is achieved. I guess I will look for integral values and the papers as suggested by Rami.

Thanks amol

[Robot]

Dear Rami,

I'm drawing 2D model, before doing grid independency test I need to key in 3 types of catalysts(e.g platinum-titanium oxide, platinum-aluminium oxide & platinum-carbon). My reactant are glycerol & water(steam)while my product are hydrogen , carbon dioxide & carbon monoxide gases. I had run the simulation & do the grid independency test , & it is not accurate ,what I need to do is to key in each catalyst (e.g platinum-titanium oxide) ,then run simulation & do the grid independency test , later continue the seconde catalyst & finally the third catalyst. please guide , thanks you very much.

[Rami]

Dear jamie hong,
Regardless of the specific problem at hand, grid independence means you should run the exactly identical case on different grids and check the results changes are smaller than a specified tolerance. I hope this answers your question.