# Convergence problem

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 December 23, 2000, 04:56 Re: Convergence problem #21 I. Dotsikas Guest   Posts: n/a Hi, John I didn't read your answer to manjgi question. Actually I said one more time what you have already said, while using not as many words as you did. One small addition: the best way to lower your Reynolds number is to increase your density. You might use very very very high densities. In this case your code MUST work. If not try to find the bug. best regards Jannis

 May 8, 2009, 09:57 y+ #22 Senior Member   Join Date: Mar 2009 Posts: 138 Rep Power: 9 Hello Everybody! I am also struggling with convergence problems, so I found this thread. Now I have some question to Y+ (1) As I was told and (by the way: what is y?) So y+ is part of the solution and not a attribute of my mesh? According to that y+ is also conditioned by my boundary conditions? (2) Which Size should y+ have? I was told y+ <1. In this thread it is suggested 50

 May 9, 2009, 14:59 #23 Senior Member   Ahmed Join Date: Mar 2009 Location: NY Posts: 251 Rep Power: 10 Yes, a lot of analysis faces convergence problems, the way to solve this kind of situations is straight forward. Convergence is a mathematical concept, and if you carefully look at any analysis technique (in the context of CFD) and if it is a Finite Element, Finite difference or Finite Volume, there is one common base line, all these techniques lead to the formation of a matrix that has to be solved. Ask yourself What causes a matrix to be solved or not and what can be done to ease the difficulties then you have the answer to your original question. Yes, the aspect ratio as mentioned in a previous post, is a very important factor (think in terms of the matrix you are solving). Cheers and good luck.

May 9, 2009, 15:42
#24
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Jed Brown
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Quote:
 Originally Posted by Ahmed Ask yourself What causes a matrix to be solved or not and what can be done to ease the difficulties then you have the answer to your original question.
While implicit methods tend to spend the majority of their time solving linear systems, your linear solver is broken if it doesn't converge. A nonlinear solver can be functioning properly and still fail to converge for your nonlinear system. The most commonly used globalization methods are line search and trust region. Such algebraic globalization is provided by any serious nonlinear solver. More difficult problems require continuation methods that exploit problem structure. Common examples are arc-length continuation and pseudo-transient continuation. For more on these methods, see

Quote:
 @book{allgower2003inc, title={{Introduction to Numerical Continuation Methods}}, author={Allgower, EL and Georg, K.}, year={2003}, publisher={Society for Industrial and Applied Mathematics Philadelphia, PA, USA} }
and

Quote:
 @article{coffey2003ptc, author = {Todd S. Coffey and C. T. Kelley and David E. Keyes}, collaboration = {}, title = {Pseudotransient Continuation and Differential-Algebraic Equations}, publisher = {SIAM}, year = {2003}, journal = {SIAM Journal on Scientific Computing}, volume = {25}, number = {2}, pages = {553-569}, keywords = {pseudotransient continuation; nonlinear equations; steady-state solutions; global convergence; differential-algebraic equations; multirate systems}, url = {http://link.aip.org/link/?SCE/25/553/1}, doi = {10.1137/S106482750241044X} }

 May 10, 2009, 16:31 #25 Senior Member   Ahmed Join Date: Mar 2009 Location: NY Posts: 251 Rep Power: 10 Jed I patiently googled for the paper till I located a ps file that I downloaded and read. what can I say? too much mathematics. In solving a matrix, simple arithmetic operations of division, multiplication and subtraction are involved and if these operations fail, the solution is difficult to arrive at. let us see:- 1- Well posed physical problems never lead to singular matrices. 2- near singular matrices are difficult to solve so what applied scientists can do in order to avoid near singular matrices? The only tool we have is the mesh quality. Boundary conditions are imposed by the physics they represent Or to say it in other words, can a mesh with aspect ratio of 2 or higher lead to a matrix that converge at the same rate as a matrix representing a mesh whose aspect ratio is 1.1 or 1.2 I am not trying to over simplify the problem, just I want to use a language that is understood by every one involved in a serious real world cfd analysis. Cheers and good luck to all

May 10, 2009, 17:02
#26
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Ahmed
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Quote:
 Originally Posted by camoesas Hello Everybody! I am also struggling with convergence problems, so I found this thread. Now I have some question to Y+ (1) As I was told and (by the way: what is y?) So y+ is part of the solution and not a attribute of my mesh? According to that y+ is also conditioned by my boundary conditions? (2) Which Size should y+ have? I was told y+ <1. In this thread it is suggested 50
Check the book by Panton (incompressible Flow), read the chapter on the development of the law of the wall. Then check the graph representing the law of the wall. Caramba, leer y entender lo que estas leyendo.

May 10, 2009, 23:49
#27
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MrFluent
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Quote:
 Originally Posted by I. Dotsikas ;12144 Hi, John I didn't read your answer to manjgi question. Actually I said one more time what you have already said, while using not as many words as you did. One small addition: the best way to lower your Reynolds number is to increase your density. You might use very very very high densities. In this case your code MUST work. If not try to find the bug. best regards Jannis
I am not very sure for what caused your diveregence but for a solver the difference bwteen using wall function and not using it is this.

For wall cells the velocities are known thus you know the convection terms. Usually flux is zero. So convection terms are zero.

Now for the diffusional terms you have no idea how to get them. So a simple way is to assume a linear profile and find out shear stress by formula
tw = visc * (du/dy).
For this you know viscosity and du/dy can be obtained by velocity profile.
However the main issue is that if profile is not linear where you cell center is the above formula gives wrong shear stress. So log wall law is proposed. And used for calculating shear stress.

If k and omega are used in calculating y+ u+ etc, wrong values of k omega could cause diveregence.
So very fine mesh and with no wall model may be more stable.

May 11, 2009, 07:05
#28
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Jed Brown
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Quote:
 Originally Posted by Ahmed Jed In solving a matrix, ...
You seem to have completely missed my point. Globalization is hard due to nonlinearity. If you have a problem solving a linear system, it almost always means that you have blown the preconditioner. Sometimes a direct solve is the only thing that works reliably, and even they fail in rare cases, but this normally triggers an error. Most causes of a nonlinear solver failing to converge will not be fixed even if the Jacobian is solved exactly.

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