Pseudo-transient solution

Hoppe · July 18, 2016, 23:01

Hello, I am trying to model a 3-d heat sink. Originally, I was trying to use a steady-state solution. Every time I did this, the energy residual diverged. When I tried pseudo-transient, my solution converged. However, I don't understand what pseudo transient means or if it is applicable to this case. I know what transient is (time dependent), but what is pseudo-transient?

Zbynek · July 19, 2016, 10:09

It is basically about how under-relaxation factors (UF) are defined. One way is to define the UF explicitly for each equation. Then the value of the UF in each cell will be the same for a given equation. Another option is to use the pseudo-time stepping - you actually solve for steady-state, but the UFs are defined via false time steps. The false time step depends on the solution so it will vary as the computation advances. Since the UF value depends also on the cell size, different UF are obtained not only for different equations, but also for different control volumes. In other words, steady-state calculations can be alternatively interpreted as pseudo-transient solutions with spatially varying time steps. I personally like to use this method since it proved to be very stable.

wc34071209 · February 17, 2018, 19:03

How about the accuracy of the solver, compared with segregated solver with SIMPLE?

Quote:

Originally Posted by Zbynek

It is basically about how under-relaxation factors (UF) are defined. One way is to define the UF explicitly for each equation. Then the value of the UF in each cell will be the same for a given equation. Another option is to use the pseudo-time stepping - you actually solve for steady-state, but the UFs are defined via false time steps. The false time step depends on the solution so it will vary as the computation advances. Since the UF value depends also on the cell size, different UF are obtained not only for different equations, but also for different control volumes. In other words, steady-state calculations can be alternatively interpreted as pseudo-transient solutions with spatially varying time steps. I personally like to use this method since it proved to be very stable.

Zbynek · February 19, 2018, 06:45

Are you asking about the difference in accuracy between the coupled and segregated solvers? Both have their advantages and disadvantages. The main plus of the coupled solver is that it tends to be more stable at the expense of computational time. However, in both cases basically the same equations are solved so if you achieve a good convergence, the methods should be equally/similarly accurate. I did not do a rigorous comparison; however, I can say that for my applications (incompressible, low Mach flow with rotating zones) both methods give the same output ("the same" in the engineering sense).

ram_call · February 19, 2018, 06:59

Quote:

Originally Posted by Zbynek

Are you asking about the difference in accuracy between the coupled and segregated solvers? Both have their advantages and disadvantages. The main plus of the coupled solver is that it tends to be more stable at the expense of computational time. However, in both cases basically the same equations are solved so if you achieve a good convergence, the methods should be equally/similarly accurate. I did not do a rigorous comparison; however, I can say that for my applications (incompressible, low Mach flow with rotating zones) both methods give the same output ("the same" in the engineering sense).

To my limited experience, coupled is more costly but usually in case that segregated solvers are fluctuating, is more stable and robust. I personally first try segregated solvers at first, or just use coupled for first iterations of transient solution. In supersonic cases or complex flows, maybe coupled is better choice!

wc34071209 · February 19, 2018, 07:44

Thank you very much.

I can understand that both coupled and segregated solvers solve the same equations ,but how about the 'pseudo transient' option? Will enabling 'pseudo transient' sacrifice accuracy for stability?

Quote:

Originally Posted by Zbynek

Are you asking about the difference in accuracy between the coupled and segregated solvers? Both have their advantages and disadvantages. The main plus of the coupled solver is that it tends to be more stable at the expense of computational time. However, in both cases basically the same equations are solved so if you achieve a good convergence, the methods should be equally/similarly accurate. I did not do a rigorous comparison; however, I can say that for my applications (incompressible, low Mach flow with rotating zones) both methods give the same output ("the same" in the engineering sense).

Zbynek · February 19, 2018, 08:05

No, it will not. Using the pseudo-time step is just another way how to relax the equations. Imagine that you would use the SIMPLE algorithm with a set of explicit under-relaxation factors. Then you would run the same simulation with the explicit under-relaxation factors that are half of the previous case. You would achieve the same results, only it would take a longer time to reach the steady-state. The pseudo-time step is just another way how to define the under-relaxation factors. The governing equations remain still the same and so if your solution evince convergence, you should obtain the same results.

wc34071209 · February 24, 2018, 14:13

Thank you for your kind reply. But I remember even for SIMPLE the under-relaxation is implicit.

Quote:

Originally Posted by Zbynek

No, it will not. Using the pseudo-time step is just another way how to relax the equations. Imagine that you would use the SIMPLE algorithm with a set of explicit under-relaxation factors. Then you would run the same simulation with the explicit under-relaxation factors that are half of the previous case. You would achieve the same results, only it would take a longer time to reach the steady-state. The pseudo-time step is just another way how to define the under-relaxation factors. The governing equations remain still the same and so if your solution evince convergence, you should obtain the same results.

Zbynek · February 26, 2018, 14:44

You are right, I should not have put together explicit & SIMPLE. Explicit relaxation, also referred to as relaxation of variables, is used in certain cases, such as NITA solver. Implicit relaxation, aka relaxation of equations, is then used in, e.g., SIMPLE. You could combine both if you wished. Check Fluent Theory Guide for more info about it.
Nevertheless, my previous answer remains the same, only change "explicit" for "implicit" to make the sentences factually correct, or alternatively omit the words completely. As per my first post in this thread, pseudo-transient approach is just another way of under-relaxation. Instead of having a hard UF value for each equation, you have a method that changes the UF based on the current solution. It changes in time and space. The final result obtained using both UF approaches should be the same.

July 18, 2016, 23:01	Pseudo-transient solution	#1
Hoppe New Member Tyler Join Date: Oct 2015 Posts: 7 Rep Power: 10	Hello, I am trying to model a 3-d heat sink. Originally, I was trying to use a steady-state solution. Every time I did this, the energy residual diverged. When I tried pseudo-transient, my solution converged. However, I don't understand what pseudo transient means or if it is applicable to this case. I know what transient is (time dependent), but what is pseudo-transient? Sabomb likes this.

July 19, 2016, 10:09		#2
Zbynek Member Join Date: Jun 2016 Posts: 66 Rep Power: 10	It is basically about how under-relaxation factors (UF) are defined. One way is to define the UF explicitly for each equation. Then the value of the UF in each cell will be the same for a given equation. Another option is to use the pseudo-time stepping - you actually solve for steady-state, but the UFs are defined via false time steps. The false time step depends on the solution so it will vary as the computation advances. Since the UF value depends also on the cell size, different UF are obtained not only for different equations, but also for different control volumes. In other words, steady-state calculations can be alternatively interpreted as pseudo-transient solutions with spatially varying time steps. I personally like to use this method since it proved to be very stable. wc34071209, randolph, chek321 and 3 others like this.

February 19, 2018, 06:45		#4
Zbynek Member Join Date: Jun 2016 Posts: 66 Rep Power: 10	Are you asking about the difference in accuracy between the coupled and segregated solvers? Both have their advantages and disadvantages. The main plus of the coupled solver is that it tends to be more stable at the expense of computational time. However, in both cases basically the same equations are solved so if you achieve a good convergence, the methods should be equally/similarly accurate. I did not do a rigorous comparison; however, I can say that for my applications (incompressible, low Mach flow with rotating zones) both methods give the same output ("the same" in the engineering sense). wc34071209, ram_call and Darko like this.

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February 19, 2018, 08:05		#7
Zbynek Member Join Date: Jun 2016 Posts: 66 Rep Power: 10	No, it will not. Using the pseudo-time step is just another way how to relax the equations. Imagine that you would use the SIMPLE algorithm with a set of explicit under-relaxation factors. Then you would run the same simulation with the explicit under-relaxation factors that are half of the previous case. You would achieve the same results, only it would take a longer time to reach the steady-state. The pseudo-time step is just another way how to define the under-relaxation factors. The governing equations remain still the same and so if your solution evince convergence, you should obtain the same results.

February 26, 2018, 14:44		#9
Zbynek Member Join Date: Jun 2016 Posts: 66 Rep Power: 10	You are right, I should not have put together explicit & SIMPLE. Explicit relaxation, also referred to as relaxation of variables, is used in certain cases, such as NITA solver. Implicit relaxation, aka relaxation of equations, is then used in, e.g., SIMPLE. You could combine both if you wished. Check Fluent Theory Guide for more info about it. Nevertheless, my previous answer remains the same, only change "explicit" for "implicit" to make the sentences factually correct, or alternatively omit the words completely. As per my first post in this thread, pseudo-transient approach is just another way of under-relaxation. Instead of having a hard UF value for each equation, you have a method that changes the UF based on the current solution. It changes in time and space. The final result obtained using both UF approaches should be the same.