Hi,

I've read some articles about comparing the performance of coupled vs segregated solvers. It seems that coupled solvers perform much better when the grid is large. I just wonder why the segregated approach is still being used? I notice that some of you here has developed your own code and still use segregated approach.... Any reason not going to coupled solver other than the fact that "coupled approach is more complicated to write if compared with segreated method"???

Any papers that actually compares these two methods and found that segregated approach has advantage over coupled approach in terms of stability, convergence etc...

I really appreciate your comments... This has puzzled me for quite time.

Speaking as someone who has written both types of solvers - the primary reason that I see is that the coupled approach is used for density-based formulations applicable to compressible flow, and the segregated approach is used for pressure-based formulations applicable to incompressible or weakly compressible flow (where the equations become uncoupled). While density-based formulations using preconditioning have been developed, I don't know of any preconditioning scheme that consistently works in the limit of Mach number approaching zero. Thus there is still a need for a segregated solver approach. And actually, there is no real difference in the level of complexity involved in the writing of the schemes.

I disagree with this because it confuses two completely independent concepts: choice of primitive variables (pressure or density) and solution algorithm (segregated or coupled). Coupled solvers have been used with pressure-based algorithms by many groups, but I'm not sure about the inverse (segregated solver with density-based algorithms).

Another piece of confusion to throw in is that coupled solvers can be either implicit or explicit. For incompressible flow, an implicit coupled solver can be very helpful. All else being equal (which is rarely the case), implicit coupled solvers have the advantage that they are scalable (CPU time increases linearly with node count) at the expense of higher memory requirements.

I don't know why segregated methods are still being used, other than that they are simpler to implement and that they've been around for a long time.

Can you post a link to a pressure-based method that uses a coupled solver? I would be most interested.

Thanks

i agree with ag, for incompressible cases some times convergence with coupled solver could be very bad. but there is one more reason segregated solver is used. like, we want to use coupled solver, but the thing is our case sizes are around 3-4 million cells, i can run a 3 million case on a single machine, where as if i want to run this with coupled solver, the memory requirement are so large that, i only dream about using coupled solver with it.

further coupled solvers can work very good with highly non linear equations, but there are ways to make segregated solvers partially coupled (its desribed in FIDAP solver manual, by Fluent) and remove this advantage also.

Jonathan Wiess and Smith preconditioner, work's very well in low range, but I am getting very good result above 2 Mach with it.

coupled solver will consume too large storage space . expecially for the three dimensional problem

Hi all,

Thank you for all the response here. Can I say if storage & memory etc is not an issue for a problem, coupled solver will always perform better than segregated one? No other problems can arise if coupled approach is used? e.g. some problems will converge on segregated but not coupled solver.... Is convergence difficulty or stability issue likely to happen for an impressible flow with complex physics such as separation, reverse flow, curvature etc if coupled solver is used?

I browse the first 10 page in google and see nothing bad about coupled solver..... That further amazed me... Is it really that good?

in a hypothetical situation where memory is not an issue, using coupled solver is very good option. but in real life, memory is a big issue. to understand this , take this extreme example, if memory is not an issue, i would be running all my cases with DNS, why bother with k-e etc, so when someone asks me whether we need k-e etc turbulence models, i say yes, knowing that memory is an issue and an important issue. similarly here, if u ask us why we need segregated solver when we have coupled solver. the answer is same, we need segregated solver because, memory is big issue with coupled solvers.

memory may not be an issue with you, but if u do not need something we can not say that this thing is not needed at all.

i hope this is much clearer answer to your question.

CFX5 (and before that TascFlow) has had this type of coupled pressure based solver for a long time - see for example http://www.ansys.com/products/cfx-advanced-solver.asp

I also think that Fluent are working on a coupled pressure based solver. Currently they only have a segregated pressure based solver and two coupled density based solvers (one explicit and one implicit).

I'm sure there are many more examples both from academia and industry.

The link doesn't provide a lot of info so let me ask the question here - what happens to the equation set they use as Mach number goes to zero. As I understand it, the real issue in using coupled vs. segregated is handling the uncoupling of the equations in the incompressible limit. Does CFX use a set of equations that include pressure as a variable and then make use of preconditioning?

ag: for your info, CFX uses pressure-based coupled solver for its calculation... but I'm not quite sure of the pre-conditioning stuff as the manual doesn't mention much about it. Are you saying that coupled solver has problem dealing with incompressible flow?

Hi zxaar.... I fully understand your points here. What I wish to know is...apart from the memory/space issue, is there any other reason that makes segregated approach more favorable to use than the coupled solver?

The Navier-Stokes equations become uncoupled from the continuity equation in the incompressible limit. I have seen two techniques for dealing with this: preconditioning applied to what are being called coupled solvers in this discussion, typically density-based but sometimes using pressure as one of the variables; and segregated schemes where the coupling is introduced by means of a pressure correction equation that ensures satisfaction of the continuity equation. I have been lazy in my terminology in referring to solvers of the second sort as pressure-based, although that is not strictly correct. But my fundamental question is if there is another way of dealing with the decoupling in the incompressible limit. I am not aware of any beyond these two basic categories, and am curious as to whether CFX or any other solver offers a third.

In case of incompressible, isothermal and forced convection flow, the fluid properties are independent of temperature and pressure, the governing equations can be solved seperately and so there is no need to use the coupled solver. Also, there is no improvement in the convergence with the coupled solver for these types of the problem. At the same time, high mamory requirement. However, one need to use the coupled solver for the other flows like compressible, non-isothermal and mixed convection.

Actually one can solve the compressible equations using a segregated solver.

> The Navier-Stokes equations become uncoupled from the continuity equation in the incompressible limit.

You mean the energy equation, aren't you ?

Is it also possible to solve the mixed convection using segregated solver ?

No, I refer to the fact that the density derivative in the continuity equation disappears and you no longer have an evolution equation, but only a constraint on the velocity field. Energy does uncouple, but it becomes a trivial part of the solution.

What is your definition of mixed convection?