Can anyone explain to me converging to steady state in "psuedo-time" to solve an unsteady problem? Euler or Navier-Stokes. How exactly does the logic of this algorithm work?

Thanks,

Nick

Pour some cups of cold water into your electric kettle and start heating it. Water temp gradually rises and after some time water will boil.The water temp will not exeed the boiling point. It attains the steady state.When it starts boiling depends on the net rate of heating. This is how we can explain attaining stedy state thru transience.In the pseudo time step solution concept, the transience is not arrested numerically rather we become interested in 'when it attains the steady state'. Using pseudo time step requires proper analysis and judgement, otherwise there is chance or risk of non-convergence and divergence.

One difference between hydrodynamic simulations and thermal only simulations - the hydrodynamic solutions can actually "overshoot" the steady state values before settling down.

Regarding my earlier post:

I should have also noted that a feature of a "quasi-transient" is that the initial condition for the simulation does not have to describe a valid fluid configuration.

A "real" transient starts from an actual configuration, same as a physical experiment starts from an actual fluid distribution. The "quasi" need only be 'reasonably' smooth (handy since you don't know the actual configuration). It's the boundary conditions that determine the final answer.

If what you want is the steady state and you are not concerned about the transient state.Then you can take huge time steps to cross the transient part provided you obey the CFL condition