In CFD, grid convergence study involves both spatial and temporal discretization error analysis. In curved channels, where the fluid experiences centrifugal forces, secondary flows are formed which in turn affect mass transfer. Keeping this is view, is it necessary to perform temporal convergence along with spatial convergence? I do understand that it is always better to round off all errors in general, but under what conditions of flow does temporal convergence analysis become absolutely necessary?
Steady-state can be seen on multiple levels. For example, 60/50 Hz alternating current may be applied at a "constant" rate although the instantaneous voltage and current are varying. The same can be said of some flows. In spite of there being small-scale temporal variations (as there always are in turbulent flow), we can still characterize some aspects of the system on a larger time scale, make important observations, and draw meaningful conclusions. It's not a simple problem, but many devices have been built on this very concept, demonstrating the appropriateness and usefulness.
It is always important to insure temporal convergence. Fr this, the time step must be calculated correctly (usually the time step is a function of the flow nature and depends on the flow variables). The number of iterations per time step must be increased until convergence is achieved.
Following Ahmad's comment, there are several ways to time step, which don't have to be the same as the spatial steps. There are fully-implicit non-iterative methods (Crank-Nicholson), implicit iterative, explicit iterative, and explicit non-iterative. Don't assume that just because a method seems to work that it adequately converges before moving forward in time. One of the many ways of checking these things is to solve a similar problem having a known analytical solution for comparison.
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