# What's the difference in formulation for steady state and time-dependent modeling?

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 January 22, 2010, 19:49 What's the difference in formulation for steady state and time-dependent modeling? #1 Member   bearcat Join Date: Jul 2009 Location: Ohio Posts: 35 Rep Power: 9 Suppose we solve the hyperbolic eq(good for all cases). We have the time term and the computations match in time, explicitly or implicitly. The convergence process will look like a flow field varying in "time" from initial to final steady state. But we don't call it time-dependent or time-accurate modeling. Transient modeling should be something else. When modeling transient flow on codes like Fluent, one easily notices that the solver performs a few dozen sub-iterations after each time step advancement. But very few CFD books explain how this works, they are all for steady problems. I know it's a stupid question. But can anyone please explain a little their formulation difference? Thank you.

January 23, 2010, 07:32
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Quote:
 Originally Posted by bearcat Suppose we solve the hyperbolic eq(good for all cases). We have the time term and the computations match in time, explicitly or implicitly. The convergence process will look like a flow field varying in "time" from initial to final steady state. But we don't call it time-dependent or time-accurate modeling. Transient modeling should be something else. When modeling transient flow on codes like Fluent, one easily notices that the solver performs a few dozen sub-iterations after each time step advancement. But very few CFD books explain how this works, they are all for steady problems. I know it's a stupid question. But can anyone please explain a little their formulation difference? Thank you.

 January 23, 2010, 08:13 #3 Senior Member   Claus Meister Join Date: Aug 2009 Location: Wiesbaden, Germany Posts: 241 Rep Power: 10 I don't understand you question too, but could your question related to Navier-Stokes-Equation or/and turbulent flow. Cheers

January 23, 2010, 11:46
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Ahmed
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Quote:
 Originally Posted by bearcat Suppose we solve the hyperbolic eq(good for all cases). We have the time term and the computations match in time, explicitly or implicitly. The convergence process will look like a flow field varying in "time" from initial to final steady state. But we don't call it time-dependent or time-accurate modeling. Transient modeling should be something else. When modeling transient flow on codes like Fluent, one easily notices that the solver performs a few dozen sub-iterations after each time step advancement. But very few CFD books explain how this works, they are all for steady problems. I know it's a stupid question. But can anyone please explain a little their formulation difference? Thank you.
1- write down the complete NS equations, the classical way
2- move the advection terms to the right hand side
3- Read the equation now
the time rate of change of phi = the total sum of the advection, diffusion and pressure gradients
4- when the left hand side is set equal to zero, then you have reached the steady state solution
In order to reach this numerical zero value, Fluent (or any other programme) discretise the left hand side by , say a first order Runge Kutta technique, and marching in small steps of time reaches the steady state....etc
the rest is explained in most books
good luck

 January 23, 2010, 13:11 #5 Member   bearcat Join Date: Jul 2009 Location: Ohio Posts: 35 Rep Power: 9 Thank you for all your reply. I think I should make the question more clear. Actually I am talking about the unsteady flow simulation, particularly for incompressible flow. People may use the techniques like "dual-time steps" or "pseudo-time-level" to compute the time-accurate flow field. This is a common topic in CFD applications but very few CFD books talk about it in detail.

 January 25, 2010, 20:30 #6 Member   ganesh Join Date: Mar 2009 Posts: 40 Rep Power: 10 Dear Bearcat, When you solve the unsteady flow equations, you attempt to update the solution at each time step, from day u^n to u^(n+1). Calculating this solution increment dU itself is a system of equations when considering the more popular and fast implicit schemes. You end up in solving linear systems using iterative solvers (such as Krylov solvers in every Newton iteration or relaxation schemes like SGS after approximating the Jacobian) which are seen as sub iterations at every iteration in physical time. With a suitable accuracy for the time--stepping scheme, this provides for a time-accurate computation, that is of importance for accurate transient simulations. Hope this helps Regards, Ganesh

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