I wish to compute a flow in a Vehicle passenger compartment....I will consider that problem as unsteady problem.... My question is ... If the solution is not converged in some time step from the calculation, but in my target time the solution is converged, can the solution be considered correct solution?... could you give me a reply....? Thank you...

If you define a problem as an un-steady flow problem, then you need to solve a set of un-steady state equations. There, the time step is fixed for every cell or volume, and you simply march the solution in time.( solution at every time step is your solution.) In this case, the final solution may or may not be a steady state solution. If you are solving a set of steady state equations, there is no way to get the un-steady solution. If you can not obtain a convergent solution from a set of steady state equations, you simply do not have a solution at all.

By some numerical methods of CFD, e.g. pressure correction method, you must get convergence for each time step. If you do not get convergence in some steps, you lose then the physical reality of the transient process, no matter you get the convergence in the final time step. But the critical point here is how you define convergence. You can loose the convergence conditions, e.g. by increasing the error limit, to get a convergence with some quality.

X. Ye

If the transient process you are simulating will have a strong influence on the possible steady-state solution (is there more than one solution possible ?), you have to ensure that any timelevel represents a "correct" (transient) solution. Usually you ensure this by providing "proper" convergence criteria. So, if you are sure (!) that your solution is of such kind, and your convergence criteria are selected in such a way, that they lead to a correct transient solution, loosing convergence at even one timelevel will result in a "wrong" steady state solution.

On the other way, if you are interested in the steady state solution only, and are sure that only one solution is possible, you don't care about the transient process - as long as the solution has converged (by some "proper" criteria).

To ensure the quality of your solution, you could do some more computations by a) changing convergence criteria, b) refining the discretization in space, c) refining then discretization in time.

You should not forget that the people in your car are moving a bit all the time. There might be also some more effects, who have an influence on the solution (the sun shines from the left or right side ???).

With these points in mind I would't care to much about a not convergent time step.

Joern

(http://www.beilke-cfd.de)

This is a convergency problem of partial differential equation with initial conditions. The answer is clear. For most transient equations, a convergent result will never reach the real solution if the initial conditions are not correctly given. In the meantime, there are also some special cases where the initial conditions are not important, typically, steady or periodically unsteady problems.

For steady or periodic problem, initial condition is only related to the numerical stability and convergent rate but has nothing to do with the final converged solution. While for non-periodically unsteady problem, the initial condition may be more important than boundary condition, and the converged solution must be obtained at each time step.

Please read some textbook of numerical method.

you can split your unsteady problem in a number of steady problems. Every steady problem must converge by themself, only then may the next time step solution converge to the correct solution. If any of your "steady" state part problems does not converge you have indeed a problem. Try smaller time step or change you converge criteria or refine your computational space. If your steady stady solutions converge by themselves but do not converge in the same solution then you have a part solution of your Problem. You have to consider if it is possible to obtain a steady state solution at all, if you can invent so much computational time in order to get an solution over a greater time interval and if you really need such a solution.