Sir,

Im a beginer in cfd. Cn anyone tell me the

1.difference between FINITE ELEMENT AND FINITE VOLUME METHODS.

2.Which one is more accurate?

3.Any link in the internet.

Ill will be greatful if you explain in very simple as im very much a beginner.

I think, u can learn it in CFD - The Basics with Applications by Anderson J.D it is a thrilling field,,but u must have patience,,, till u kn the basics,, i think

There have been many discussions on this topic already. Try seraching the forum using appropriate search terms. I'm sure you will find many existing and useful thoughts here.

Prajeesh wrote:

Im a beginer in cfd. Cn anyone tell me the

1.difference between FINITE ELEMENT AND FINITE VOLUME METHODS.

2.Which one is more accurate?

3.Any link in the internet.

Ill will be greatful if you explain in very simple as im very much a beginner.

-----------------

diaw's reply:

Both methods are provide approximate solutions to the governing equations of fluid motion. Each method has its share of advantages & disadvantages - as can be found in most literature on the subject.

The accuracy is more dependent on the modeling approach than on the methods themselves. FV methods tend to be a little more stable, but provide less detail than traditional FE methods. More detail means greater computing cost - with potentially higher accuracy.

As a good start, you could begin with traditional FVM's (Patankar) & then work your way onto FEM (Zienkiewicz, Taylor).

Enjoy, it is a fascinating topic. When you've got the basics under your belt, come on & join the non-linear world...

diaw (desA)

Hi

What should be the beginning reading for non-linear fluid.

thanks nl

Neo Lim wrote:

What should be the beginning reading for non-linear fluid.

-------- diaw's reply:

Neo, my comment had more to do with the non-linearity within the momentum (Newton's 2nd law) equations themselves, than for non-linear fluids. Understanding the implication of the transient quasi-linear equations of motion for the simplest of fluids - Newtonian, incompressible, is a major starting point.

Once the vagiarities of this basic system are better understood, then the implications of slight compressibility & non-newtonian (powerlaw etc) fluids can be better understood.

That said, I would direct you towards mathematical chaos, bifurcations, resonance in say Journal of Chaos, Solitons & Fractals. This will begin to give you some insights into what is emerging in the Mathematical research. Engineers & fluid dynamacists are still playing catch-up in this regard. The fascinating part is understanding the 'wave nature of the navier-stokes & continuity equations'. That there are wave-phenomena active within our CFD domains is a given - in fact, we need to re-capture some of the wave phenomena that our numeric integral-based methods damp out. (I'm in the process of publishing a paper in this regard & hope to upload a preprint to my website within a few weeks. This will explain some of this material).

This emergent non-linear field is fascinating & provides a fertile research area.

An excellent book explaining the mathematic existence of parabolic waveforms is by Volpert (search for the AMS free download by A.Volpert & his sons. This is truly excellent.)

Another useful source of non-linear research is the 'Advanced Series in Nonlinear Dynamics', by World Scientific.

There are a few books in nonlinear wave research written by a number of excellent Russian scholars. Wisem's name springs to mind. The problem is that they do not seem to have been translated into English.

I hope this helps.

diaw (desA)

hi diaw,

Thank you for your wonderful introduction. I have some more doubts that may need help.

1. In subject of non-linear dynamics (eg Non-Linear Fluid Dynamics), to my knowledge mathematicians play bigger roles than engineers does. So it gives the impression that engineers somehow lack sound mathematical foundation. My experience with engineering people, also indicates that Engineering People avoid such heavily mathematics subject like Non-linear NS equation. So my question is "Can engineers (who have usual engineering background) be on this subject?"

2. I also preferred to know the level of mathematical sophistication demended for working on this subject. ie "Are solid foundation on Mathematical Analysis, Functional analysis and Principles (theory) of ODE and PDE required?"

I was interested amazing subject of non-linear. But above questions still not clear making me very far away from non-linear fluid with my engineering background.

Thanks

Hi neo,

Firstly, let me try & put your mind at rest regarding Mathematics & Engineers. I am an Engineer, with base training as a physicist. The ability to 'feel' the subject physically has been important for my research.

What I have done is to add Mathematical skills as I require them. So, my mind is that of a physicist, but my toolbox is borrowed & adapted from our wonderful Mathematical friends...

You will definitely need to build up your experience with pde techniques, but frankly, the Navier-Stokes equations seem rather short of full analytical solutions at present. In fact, in most cases, fully integrable solutions are a little rare - with most solutions being of a non-integrable nature. This means that you will need to employ numerical techniques to simulate much of your research.

The problem with the current crop of most of the numerical techniques are 'designed' to press out wave solutions, although some dominant effects are able to creep through. These solvers are primarily designed to extract the slow-time response of the system. The faster phenomena can be teased out, however, with a little cunning & insight. We are going to have to adapt our numeric schemes to capture more wave phenomena if we want to model *almost incompressible* fluid flows.

So, neo, as an engineer, you can most definitely begin with what you can do best - most likely the numerics schemes & simulation. Then begin reading up on current nonlinear work that the Mathematical community is publishing. You will then be in a position to blend your two experiences & push the numerics envelope forwards, based on your insights offered from the mathematical side.

I hope this encourages you.

diaw... (desA)