# how i can solve this unsteady problem

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 September 3, 2011, 07:05 how i can solve this unsteady problem #1 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 Sponsored Links i want to solve unsteady flow around a airfoil, i solved steady viscous flow by psay and omega with iterative method before, now i want to change steady to unsteady.........please help me

 September 4, 2011, 07:06 #2 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 are you asking for help programming an unsteady solver or using an existing one??

 September 4, 2011, 09:25 reply #3 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 yes i want an unsteady solver for finite diffrences method,thanks

September 4, 2011, 14:10
#4
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Quote:
 Originally Posted by sarmadi yes i want an unsteady solver for finite diffrences method,thanks
So if I understand you correctly, you already have an explicit FD solver which you use to do pseudo timestepping to steady state? if that's the case, you are almost already there...

 September 5, 2011, 02:41 ok #5 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 ok, i have a code that solve steady state flow FD , but now i want to solve unsteady state flow with FD and be expllicit,thank you, do you have it?

 September 5, 2011, 03:10 #6 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 No, I don't, but if you already HAVE a FD code which solves the time integration in a pseudo timestepping, you are done....that's why you need to state what time integration you use in your steady state solver! Two options: a) pseudo time stepping in an explicit way -> you are done b) implicit i.e. matrix solver -> you need to post back and I will try to help you!

 September 5, 2011, 03:20 #7 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 ok, i use iterative method like LSOR or gous method for solving psi and omega in steady state

September 5, 2011, 03:30
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Quote:
 Originally Posted by sarmadi ok, i use iterative method like LSOR or gous method for solving psi and omega in steady state

I guess you mean "Gauss" Could you tell me what psi and omega are? I'm not familiar with that notation....

Here is what you have to do: the equation you want to solve is/must be written in differential form, sth like:

du/dt + a du/dx + b du/dy = s, where u can be a (x,y) vector). Explicit timestepping goes as follows: Write the above equation as

du/dt +R(u) = 0, where R(u) is called the residual, i.e. the spatial operator. Now use your code and identify the parts where R(u) is evaluated. Note that R(u) must be evaluated at t=n, so at the given/known time step.

so evaluate R(u) at u=u(n) and plug that into du/dt=-R(u). At that time, you have turned your PDE into an ODE.
Now just integrate the ODE in time, the simplest would be by an Euler approach:

du/dt = (u(n+1)-u(n))/delta t

That gives you u(n+1)!

clear so far?
Cheers!

 September 5, 2011, 03:51 #9 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 ok, it s time that i clear my mean for you i have navier stokes equation for solving that includes: momentum and continuety eqn. one method for solving them is using vortisity yhat is du/dy-dv/dx=w; and using psi that have gradiant^2(psi)=-w; so i have two elliptic eqn for steady state manner that should solve together; when i chang it to unsteady manner i have an elliptic eqn and a parabolic eqn and i need to solve them together but i dont know how?????? thank you

 September 5, 2011, 05:37 #10 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 Well, you have to write your equations in that form (just 1d, scalar example): du/dt + R(u)=0, where all the spatial derivatives go into R(u). That can be first, second, or any order derivatives..... just group them all together, and approximate them with your finite differences in the way you know! Then, you get an ODE in time (for psi and vorticity e.g.). You can solve that ODE in a time stepping way, like an Euler or standard Runge-Kutta approach (given that your whole discretization is stable!).

 September 6, 2011, 02:37 #11 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 thank you for trying, my problem is that my both eqn are dependent to each other

September 6, 2011, 04:00
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Quote:
 Originally Posted by sarmadi thank you for trying, my problem is that my both eqn are dependent to each other
uh...... Navier Stokes equations or Euler equations are also dependent on one another... so I guess I don't understand your problem??

 September 6, 2011, 07:43 dont be confused #13 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 please calm down, it is not confusing problem so consider you want to solve unsteady flow around an airfoil(Naca 12) and this flow is viscous and incompressible and laminar before that i solve steady flow for cavity

September 6, 2011, 07:53
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 Originally Posted by sarmadi please calm down, it is not confusing problem so consider you want to solve unsteady flow around an airfoil(Naca 12) and this flow is viscous and incompressible and laminar before that i solve steady flow for cavity

ok, I'm all relaxed again :=)

I guess I don't understand your remark from above:

my problem is that my both eqn are dependent to each other

If you solve the NS equations in standard formulation (rho, u,p...), your equations are (of course) dependent on each other, as for example the rho-equation contains terms with u,v,w in them. If you reformulate the NS equations in terms of vorticity and other quantities, the equations are again dependent on each other...

So that doesn't introduce any new problem, right? You can solve your NS equations in your formulation in the same way you would solve them in any other formulation....if you use explicit timestepping, that's easier than for implicit...

 September 6, 2011, 08:16 #15 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 yeah now plz answer me??? how i can impose time step and solve iterative????

 September 6, 2011, 08:25 #16 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 Ok, I will try again: Write your equation as du/dt +R(u)=0. R(u) contains all spatial derivatives. U is your vector of solution variables, so vorticity and whatever else for you. 1) You start at timelevel 0 with your initial solution/projection. So you know U at t=0. compute R(U(t=t0)) with that information. 2) Now look at du/dt = -R(U(t=0)). Compute du/dt from 1) (trivial, just minus) 3) discretize du/dt in any way you choose. Look up ODE solvers, but standard are Runge Kutta schemes. Let's say you picked du/dt = (u(n+1)-u(n))/delta t. n+1 = solution at NEW time step, n= solution at time step t=0, the one you know from your initial condition. 4) so you have: u(n+1)=u(n)-delta t * R(u(n)). Compute u(n+1) from that -> that's your new timestep 5) repeat this procedure till you reached your final time... Did this help? cheers!

 September 6, 2011, 08:34 #17 New Member   parisa Join Date: Sep 2011 Posts: 10 Rep Power: 7 yes, i know what you say and it is completly true. so in U i have pressure how i update it????

September 6, 2011, 08:54
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Quote:
 Originally Posted by sarmadi yes, i know what you say and it is completly true. so in U i have pressure how i update it????
Ok, good question...you would have to compute the pressure from your state variables, so vorticity and the other thing in each step. I haven't done this before, there might be an easier way. I suggest you ask your professor, he or she should know!

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