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 Herrold January 31, 2008 22:11

basic questions on residuals

1. What does oscillating or flat residuals indicate. Why the convergence criteria is set on 1e-04, why not on 1e-06 or 1e-03.

2. Why do we say solution has converged. Is it because variables like velocity etc stop changing or is it because fluid has flown in and out of our problem domain?

Thanks for your answers or any input.

Herrold

 ganesh February 1, 2008 08:23

Re: basic questions on residuals

Dear Herrold,

1. Flat residuals indicate that the solution is stationary with respect to time and converged to steady state. Oscillating residuals could arise because of limiters and then it is necessary to look at integrated quantities for declaring convergence. Oscillating residual DOES NOT necessarily mean that steady state cannot be achieved.

The choice of tolerance depends on the user and the problem, there is nothing special about the value used, but 1e-6 is generally preferred.

2. Convergence of the solution refers to the fact that flow quantities and associated integrated coefficients do not any longer depend on time, and steady state is achieved. For an unsteady problem the integrated coefficients will achieve a stationary pattern, wherein the code is stopped. Fluid is always flowing in and out of the domain, what we are interested numerically is to obtain the solution to this flow problem.

Hope this helps.

Regards,

Ganesh

 Herrold February 1, 2008 13:53

Re: basic questions on residuals

Thank you very much for your responce Ganesh. You have cleared up quite a few doubts of mine.

Regards Herrold

 adam February 3, 2008 11:12

Re: basic questions on residuals

Hi Ganesh

I would like to follow up on what you told Herrold.

1. I did not quite understand what you meant by limiters? You said that choice of tolerance for residuals depends on user and the problem, but 1e-06 is generally preferred. However the codes i have worked with use 1e-04. I guess what i am trying to ask is how a tolerance number affect the steady state of a flow.

If i use 1e-04 as my tolerance that would indicate that my flow is less steadier than if i use 1e-06. Is that what these numbers indicate?

2. You said that convergence of the solution refers to the fact that flow quantities do not any longer depend of time and steady state is achieved.

Why do we have to achieve this steady state. We can still obtain velocity at a particular point in our domain even when its changing with respect to time. Moreover, why do we take the trouble of introducing time derivative in our Navier-Stokes equations in the first place when we want to achieve steady state at last.

Its always pleasure to hear and learn from you.

Regards Adam

 adam February 3, 2008 13:33

Re: basic questions on residuals

One more thing. Some times people run unsteady problem but initialise it with steady state solution. In such case fluid has already achieved steady state then why run it as unsteady. I am very new to CFD i hope you wont mind asking you so many questions.

Regards Adam

 Mayur February 4, 2008 02:12

Re: basic questions on residuals

I strongly feel that you need a basic course in Fluid Mechanics. Without that using CFD will make no sense to you.

 adam February 4, 2008 07:27

Re: basic questions on residuals

Thanks for your answer Mayur. Can you suggest me any book or material that you had for your course.

Regards adam

 Mayur February 4, 2008 09:27

Re: basic questions on residuals

Introduction to Fluid Mechanics, 6th Edition Robert W. Fox, Purdue Univ. Alan T. McDonald, Purdue Univ. Philip J. Pritchard, Manhattan College

This is a good place to start. though you need to be good in mathematics if u want to understand this all by itself. I would suggest is that you go through this book skipping anything you don't understand.

 adam February 4, 2008 12:25

Re: basic questions on residuals

Thanks Mayur. I have learnt basic fluid mechanics. I am trying to learn computational fluid dynamics. By the way do you have an answer to any of the questions that i have posed on forum. I am more interested in obtaining results than understanding the the physics of fluids at the moment. I can do that by giving some numbers to computers and receive an output. I know hundreds of such fluid mechanics books. Thanks anyway

adam

 Mayur February 5, 2008 02:33

Re: basic questions on residuals

you may have learnt basic fluid mechanics and you may know thousands of books but the question you have posted shows that you don't have any understanding of the basics. Doing a course and developing a basic understanding are two different things.

 adam February 5, 2008 07:15

Re: basic questions on residuals

It seems like you dont know the answers to any of my questions either. We should do the course together! If i give numbers to computer it will give me results. I know exactly what i need to know and learn. You sound confused.

adam

 adam February 5, 2008 07:36

Re: basic questions on residuals

By the way i did not mean to insult you. I really appreciate you for the time you have taken out to answer my post. Its just that i am trying to know something about CFD and i dont think going back to basic fluid mechanics would be of any help. You may disagree with me and you are entitled to do so. Thanks again

Adam

 PKN February 5, 2008 10:08

Re: basic questions on residuals

Hi adam & Ganesh,

I'm new to CFD . Ganesh's reply & adams questions have really enlightened me . I have understood few basic things that I need to learn rather think & understand than simply simulating.

Thanks a lot!

 Mayur February 5, 2008 10:18

Re: basic questions on residuals

Well even I was not trying to insult you !!! I will try to answer your question with the understanding that you already know the basics.

See the most fundamental equation in Fluid Mechanics is Navier-Stokes equation. As you know it is a system of coupled partial differential equation and for the general industrial problem has no analytical solution. So we try to calculate the solution numerically using a computer. For this the Big domain is broken into small control volumes. The partial diff. eqns are intergrated over this small control volume(Finite volume approach) to yield linearized ALGEBRAIC equations with the velocity, pressure and temperature as variables. Thus we now get a system of ALGEBRAIC equations to solve to get the result. There are various ways to solve this system of equation. The easiest way is to start with a guess solution and use the equations to refine the values of the variables. This method is called iteration. After a lot of iterations the values of the variables almost satisfies the system of algebraic equations and we call the solution converged.

This was a very crude explanation but hopefuly it is of some help !!!

 adam February 5, 2008 16:02

Re: basic questions on residuals

Hi Mayur

Thank you so mcuh for answering. I had asked Ganesh following two question.

1) If i use 1e-04 as my tolerance (for residuals) that would indicate that my flow is less steadier than if i use 1e-06. Is that what these numbers indicate?

2) why do we take the trouble of introducing time derivative in our Navier-Stokes equations in first place when we want to achieve steady state at last. I understand sometimes steady case does not converge unless we introduce a time derivative in it. But why is this so?

What you have described above is a discretization procedure of navier stokes equations. Unfortunately answer is not there! I still appreciate the effort you have made.

Moreover, you can flip through every page of the book that you had recommended to me, you would not find answer to my questions.

Regards adam

 Mayur February 6, 2008 01:44

Re: basic questions on residuals

1. As I have said earlier the resulting solution satisfy the algebraic equation only approximately. It is never an exact solution. The deviation is measured by residuals. If residuals is large it means that it is a less accurate solution. So a residual of 1e-6 means it is a more accurate solution than 1e-4 but it will take a longer time to reach that stage.

2.In steadt state the time derivative term is ignored in FVM. In FEM it is kept for stability purposes but at convergence that term approaches zero.

hope it helps.

 adam February 6, 2008 06:39

Re: basic questions on residuals

Ok thanks that helps! I still dont think i need to go back to basics (my opinion) and you recommended wrong book to me. Can you recommend something that has more relevance to what i am doing right now.

Regards adam

 Mayur February 7, 2008 02:54

Re: basic questions on residuals

Maybe u can go through fluent Users manual in detail if you have access to it.

The sad part in CFD is that there is not a single good book in it that covers everything. Mostly u have to attend lectures/classes and on-job training and experince. Long ago there was a good book... something like Numerical Heat and Mass transfer by Suhas V. Patankar... but long time back it has stopped being published because of some dispute between autor and publisher... if u find it from any professor u can go through it.

 adam February 7, 2008 07:28

Re: basic questions on residuals

ok thanks Mayur. take care

Regards adam

 A.pranesha setty February 9, 2008 01:20

Re: basic questions on residuals

I had one problem on one dimensionak heat equation which can be solve by the method of residue.and in that problem i am getting some error function i dont know how to solve that problem can u give me details how to send that problem to ur mail id plz send me ur mail id

thank u sir

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