# Why is there an under-relaxation factor for density and body forces?

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 October 25, 2018, 14:55 Why is there an under-relaxation factor for density and body forces? #1 Member   Mostafa Join Date: Sep 2016 Posts: 30 Rep Power: 8 Hello everyone, I'd be thankful if someone could explain why there's an UR for density and body forces when density is constant and there's no gravity. In addition, I can comprehend why UR for density exists - for the case when density changes with temperature or pressure. Hence, there's an additional equation that's solved for the density alone. But why is there an UR for body force when they're only calculated by the product of gravity (constant) and density (calculated)? I've looked everywhere but couldn't find an answer. So I'm really grateful for anyone looking to help. Thank you.

 October 26, 2018, 10:15 #2 Member   Mostafa Join Date: Sep 2016 Posts: 30 Rep Power: 8 Anyone? Pretty please :'(

 October 26, 2018, 11:03 #3 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,146 Rep Power: 61 Why is there a urf for density for a constant density case? You can call it laziness from the Fluent developers when they created the GUI. These settings still exist as text lines in the .cas file whether you see them or not in the GUI. Having them shown regardless is being transparent. Maybe you like the black box approach better? Then it's just a matter of preference. The body force is primarily for multi-phase problems. Body forces can be & some are treated implicitly in Fluent similar to how implicit under-relaxation of equations are used (notice the urf name is momentum and not velocity). Brief explanation of under-relaxation of equations. At each iteration, a relaxed equation is solved. This approach is very different than simply applying a urf to a variable and limiting the change in a variable from iteration or iteration. A limited amount of body force is injected into the correction equation during SIMPLE. There is a note that this implicit body force treatment is done here, but no actual example equations are given in the manual. bikooo3878 likes this. Last edited by LuckyTran; October 26, 2018 at 12:57.

 October 28, 2018, 02:04 #4 Member   Mostafa Join Date: Sep 2016 Posts: 30 Rep Power: 8 I've captured a screenshot as soon as you replied and have been discussing it with my colleagues since then. With your edit, it makes much more sense. Now I'm just puzzled between implicit and explicit urf. If you'd only assure me that not all flow urf are always implicit. That is, the density urf is an explicit one, since it there's no implicit equation needed to calculate it. Turbulence quantities are similarly explicit. They are both calculated with pressure and velocity values at the same node. Energy, on the other hand, is an equation to which we input an implicit urf. Body forces depend on the nature of the problem. If I'm wrong, I'd be grateful if you corrected me. Thank you.

October 29, 2018, 14:09
#5
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Lucky
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Explicit/implicit in relaxation has a different meaning than explicit/implicit solver.

Explicit relaxation means you relax the variable. This means you solve an equation and instead of taking the full update, you take only a partial update of that variable. Let's say you start with x=1 and you execute your algorithm (and do a bunch of calculations) and at the end of everything your algorithm says that the solution should be x=2. If my explicit urf is 0.5 then instead of taking x=2, I would take x=1.5 as the final solution for this iteration.

Implicit under-relaxation means you relax the entire equation. This means

that at any iteration, you don't actually solve the equation but a relaxed equation. Here I cannot say whether the solution should be x=2, because instead of solving the equation which would've given be x=2 as the solution, I solve a relaxed equation, which can produce any other result.

Both variables and equations can be relaxed and both can be applied simultaneously. For example, I can apply implicit relaxation to the momentum equation and apply explicit relaxation to the velocity. Another practical example (and you can find this happening in Fluent) is with the energy equation. I can apply implicit relaxation to the energy equation (and solve for enthalpy/internal energy using the relaxed energy equation) and instead of directly calculating temperature from the equation of state, I instead apply explicit relaxation onto the calculation of temperature. This guarantees that me temperature will always be inconsistent with the internal energy or enthalpy, but I do it anyway because it improves stability.

If you use the COUPLED solver in Fluent, you'll find more examples of both implicit and explicit relaxation applied one on top of the other.

Quote:
 Originally Posted by bikooo3878 That is, the density urf is an explicit one, since it there's no implicit equation needed to calculate it.
Not necessarily true because you solve the continuity equation for density.

Quote:
 Originally Posted by bikooo3878 Turbulence quantities are similarly explicit. They are both calculated with pressure and velocity values at the same node.
Which turbulence quantities? Quantities like k and omega or k and epsilon have transport equations and these are solved using the transport equations. k and epsilon are not calculated from pressure and velocity. These equations have implicit relaxation applied. The turbulent viscosity on the other hand does use explicit relaxation.

Body forces are like source terms in the momentum equation. You don't have to inject the full amount of the source term into the equation. It is possible to apply implicit relaxation to a single term.

So it's not correct for me to say that implicit relation always refers to an entire equation. The difference is that implicit relaxation relaxes the equation you solve (i.e. it changes the coefficient matrix). Explicit relaxation means you solve an equation and don't take the full update.

All equations can have implicit urf's. All variables can have explicit urf's. The question is, for a particular solver, how many are applied?

October 29, 2018, 14:25
#6
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Thank you for your clear answer. It really has helped me a lot.

Quote:
 Originally Posted by LuckyTran It is possible to apply implicit relaxation to a single term.
This is the only thing I couldn't understand. implicit relaxation is applied to the whole equation (it changes the factors), how can I apply an implicit relaxation to a just single term? Is it like injecting part of the old value in the source term?

Sorry if this is a dump question

Thank you.

October 29, 2018, 16:43
#7
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Lucky
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Quote:
 Originally Posted by bikooo3878 Thank you for your clear answer. It really has helped me a lot. This is the only thing I couldn't understand. implicit relaxation is applied to the whole equation (it changes the factors), how can I apply an implicit relaxation to a just single term? Is it like injecting part of the old value in the source term? Sorry if this is a dump question Thank you.

Yes, implicit under-relaxation is like injecting a part of the old value into the equation for the new value. Under-relaxation of an entire equation looks like so, specifically you should look at (18.4-23). The difference is phi is more than just one thing. You can split phi up into its parts and apply a different urf for each part (different alpha's). There isn't a rule that says you have to apply the same under-relaxation (the same alpha) to every term. That is, you can group terms by physical meaning (advection, diffusion, source, body force) and apply different alpha's to each.

(18.4-2) also gives you an idea of physically what is happening when you apply implicit under-relaxation. It's as if the solution steps in time a certain amount (local cell time). When you apply different urf's to each term, it's as if each term (say the advective term, vs the diffusion term, vs the body force term) advances the solution in time by different amounts.

 October 30, 2018, 12:42 #8 Member   Mostafa Join Date: Sep 2016 Posts: 30 Rep Power: 8 Well this explains a lot Can't thank you enough

 Tags body force, density, fluent, under relaxation factor