As we were taught in basic fluid mechanics, steady flow is independent of time. Why do we need to specify timesteps even for steady state simulation? (in some softwares it is calculated automatically! But my question is why is it required in first case?)

Dear Srikanth,

The Euler equations at steady state show a mathematical behaviour which is a function of the mach number. Thus, it turns out that the equations are elliptic in the subsonic regime, hyperbolic in the supersonic regime. In applications involving purely subsonic or supersonic flows, therefore specific elliptic or hyperbolic solvers can be used, but in transonic regimes, where the flow could accelerate from subsonic velocities to supersonic ones, the behaviour of the equations will also change accordingly. This make use of steady solvers near to impossible, as some regions will have subsonic M, others supersonic M. However, it turns out that with an added time derivative to the steady state equations, the unsteady Euler equations are always hyperbolic, independent of M. Add to this the nicety of hyperoblic pdes and their solution procedures, we get a single solver that can be used for any mach regime. Steady state is often decided when some norm of the time derivative falls below a prescribed tolerance, say 1e-8.

Hope this helps

Regards,

Ganesh

Thanks Ganesh... I had a faint idea but you have given the complete explanation!!!

Dear Ganesh,

Incase we are to develop a solver for completely elliptic pdes,( subsonic regime) , do you mean to say that it can be done without specifying timestep?

Dear learningCFD,

For a completely subsonic steady state problem, you can as well have a steady elliptic solver, since the solution needs to be time--independent. But, you can also opt for the unsteady version, stepping in time and drive the solution to steady state.

Hope this helps

Regards,

Ganesh