[cfdnewb123]

I am referring to the book by H.K.Versteeg and he mentioned the following modifications,
1) Adding a^0_P to the central coefficient a_P
2) Pressure correction equation must include the unsteady continuity equation effect (rho^0-rho)*DV/Dt. However, since I am using incompressible flow, I just assume this as zero.
3) The time-stepping procedure creates an extra loop outside the main iteration cycles of SIMPLE.

I am confused by the third step as I thought that the iteration step of SIMPLE to convergence can be used as the time-stepping procedure. However, my thought is not correct as the solver produces different convergence result when different dt is used, which I think is the solver converging after making that particular timestep. (Smaller dt gives a less varied result)

Hence, does this mean that for n-number of timesteps, I need to make n-number of SIMPLE solver convergence? If yes, how do I add this time-stepping loop outside the SIMPLE solver? The SIMPLE solver already gives me the corrected momentum & pressure for the next timestep already and thus, what do I need to do outside the SIMPLE loop while inside the time-stepping loop?

[LuckyTran]

Originally Posted by cfdnewb123

I am confused by the third step as I thought that the iteration step of SIMPLE to convergence can be used as the time-stepping procedure.

It can indeed be interpreted that way if you know what the local Courant numbers are. SIMPLE for a steady case is somewhat analogous to transient SIMPLE with a really large (infinite) time-step. But you are now doing a transient case, so it's no longer about analogies but actually doing it.

Originally Posted by cfdnewb123

Hence, does this mean that for n-number of timesteps, I need to make n-number of SIMPLE solver convergence? If yes, how do I add this time-stepping loop outside the SIMPLE solver? The SIMPLE solver already gives me the corrected momentum & pressure for the next timestep already and thus, what do I need to do outside the SIMPLE loop while inside the time-stepping loop?

Yup. Each time-step, you need to re-solve the system which can involve many SIMPLE sweeps each time-step.

Once you add the transient terms from step 1), which will also contain a dt in it, you get a very similar linear system that needs to be solved the same way. At the end of this you get the solution at the next time-step. Then you just keep repeating this until you get to your desired solution time. The main cycles of SIMPLE needs to converge iteratively for a single time-step. Then you just march it forward in time .

[cfdnewb123]

Originally Posted by LuckyTran

It can be interpreted indeed be interpreted that way if you know what the local Courant numbers are. SIMPLE for a steady case is somewhat analogous to transient SIMPLE with a really large (infinite) time-step. But you are now doing a transient case, so it's no longer about analogies but actually doing it.



Yup. Each time-step, you need to re-solve the system which can involve many SIMPLE sweeps each time-step.

Once you add the transient terms from step 1), which will also contain a dt in it, you get a very similar linear system that needs to be solved the same way. At the end of this you get the solution at the next time-step. Then you just keep repeating this until you get to your desired solution time. The main cycles of SIMPLE needs to converge iteratively for a single time-step. Then you just march it forward in time .

Thanks for the response. However, I still don't get how to update the first converged result (from SIMPLE) to the next timestep.
My algorithm looks something like this,

for t=1:NumberTime
time=dt*t;
u0=u; v0=v; p0=p;

[u,v,p]=SIMPLE(u0,v0,p0)

end

Is this correct? I don't think so as my solver basically stuck at the first successful timestep. After one timestep when the SIMPLE produces the converged result, this converged result get "reused" by SIMPLE which basically just converge the result further. As the result is already converged, the result remains the same for the subsequent timesteps.
There is something wrong with my understanding as I don't get how to shift it to the next timestep!

[FMDenaro]

Originally Posted by cfdnewb123

Thanks for the response. However, I still don't get how to update the first converged result (from SIMPLE) to the next timestep.
My algorithm looks something like this,

for t=1:NumberTime
time=dt*t;
u0=u; v0=v; p0=p;

[u,v,p]=SIMPLE(u0,v0,p0)

end

Is this correct? I don't think so as my solver basically stuck at the first successful timestep. After one timestep when the SIMPLE produces the converged result, this converged result get "reused" by SIMPLE which basically just converge the result further. As the result is already converged, the result remains the same for the subsequent timesteps.
There is something wrong with my understanding as I don't get how to shift it to the next timestep!

Have a look to the Ferziger, Peric, Street textbooks, there is a chapter devoted to the transient method.

Furthermore, you could also think to use a fractional time step.

[LuckyTran]

You will need to keep a copy of the same initial solution at every SIMPLE iteration as well as the latest implicit solution.


You probably just didn't do 1) correctly if your solution isn't going anywhere.

[duri]

Originally Posted by cfdnewb123

I am referring to the book by H.K.Versteeg and he mentioned the following modifications,
1) Adding a^0_P to the central coefficient a_P
2) Pressure correction equation must include the unsteady continuity equation effect (rho^0-rho)*DV/Dt. However, since I am using incompressible flow, I just assume this as zero.
3) The time-stepping procedure creates an extra loop outside the main iteration cycles of SIMPLE.

Are you using three sets of variable for n, n-1 and old. The old variable is not same as n-1 except for the first iteration of each time step. At each iteration n-1 should be replaced by n till the convergence. After convergence old variable should be replaced with converged solution.

Originally Posted by cfdnewb123

Hence, does this mean that for n-number of timesteps, I need to make n-number of SIMPLE solver convergence? If yes, how do I add this time-stepping loop outside the SIMPLE solver? The SIMPLE solver already gives me the corrected momentum & pressure for the next timestep already and thus, what do I need to do outside the SIMPLE loop while inside the time-stepping loop?

This may indicate you are not keeping the old variable constant in the inner iteration and probably updating with new values.