Flow in cylinder
 

Hi every body!

I want to solve a transient, incompressible inviscid flow in a cylinder, which its initial condition is zero velocity everywhere and at delta t=1 left boundary condition is V boundary= Vb and for right boundary condition we have pressure= ambient pressure
it seems that all nodes velocities should reach Vb after 1 time step but I have problem while using conservation methods, it takes some more steps for nodes to reach Vb.
I would be so thankfull if somebody could help me.

What boundary condition do you have for pressure at the velocity inlet?

no boundary condition, I solve mass equation in inlet for pressure

What method do you use to couple velocity and pressure? Do you use some limited compressibility method or a fully incompressible method where div U = 0 ?

Is the behavior independent of time-step and Reynolds number (i.e. if you change dt or Re, will you reach Vb in the entire domain in fewer time-steps)?

I use a pressure based method, and yes its behavior is depends on delta t, by increasing time step it reaches the Vb in fewer steps. and by omitting transient term whole field velocity reaches to Vb in one step which is desired, thank you

Ok. I assume that you are solving some kind of Poisson equation for pressure and then you need a boundary condition for pressure at the inlet.

You state that you use continuity equation for this. Could you please show what you mean here?

Anyways, some methods specify a homogeneous Neumann condition for pressure at boundaries. However it might be better to use the normal momentum equation instead. By doing so you will compensate for grid size and time-step and the solution will be independent of the two. It will also converge within one time-step, given that your linear solver converges sufficiently.

first of all thanks for your quick reply, as I am really confused with it.

I solve du/dx=0 for mass and I use finite element control volume method, so I use u* and u* is pressure based and is

Mass: U*e - Uinlet = 0

u*e =( Ui+Ui+1)/2 + (Pi-Pi+1)/(2*ro*u*e)
U inlet = Vb

and
Momentum: U inlet = Vb

you mean that I need one more condition for pressure?