Does SPH solution have a steady state solution?

[siddharth...@gmail.com]

I was wondering at the steady state concept conventionally used in conventional grid based Eulerian techniques. Like cases such as Poiselluie flow where a fully flow developed profile is the steady state solution, temperature across a cantilever beam that has boundary conditions at both ends. I believe we iterate the solution until a steady state is achieved. 

In contrast for a Lagrangian based SPH technique, I am little confused as to how to know if the flow has reached steady state or not. If I have a case of nozzle flow, with very high inlet pressure of about 300 MPa, so its becomes like a jet crusing through a nozzle and coming out of it with velocities close to 800-900 m/s, with the Reynolds number of this flow, I see turbulent boundary layer at the walls. So, coming to my question for such a case like this, how do I know if the flow in the nozzle has reached steady state or not? How do I decide when the flow is reaching equilibrium? 

I am hoping to know if you all have some idea about this. It would help greatly. Thank you. 

Siddharth

[Stephan]

Dear Siddharth,

I don't know if I understand you correctly, but in turbulent flow you never have a steady state or equilibrium. In conventional Eulerian techniques you also wouldn't reach a steady state in case you perform DNS simulations. What happens most often in Eulerian techniques is that people use the RANS equations with a turbulence model to model the unresolved eddies at the smaller length scales. In that case your solution would appear to be steady because of the averaging, but in reality it is not the case. I suppose you didn't incorporate a turbulence model in your SPH simulation so in that case you won't get a steady state solution if you're looking for that I guess.

Best,

Stephan

Op dinsdag 23 november 2021 om 06:44:05 UTC+1 schreef siddharth...@gmail.com: