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solomon May 22, 2002 00:00

size of element
What could be the size of the smallest possible, practicaly feasible size of single element in CFD grid for two dimensional problem.

Alammar May 22, 2002 13:24

Re: size of element
Don't forget "continuum".

solomon May 23, 2002 01:38

Re: size of element

I do not understand when you say do not forget continuum. I wanted what the size of the fine grid element one can practicaly generate in any unit. Certainly one can not make it smaller than some value. There must be a limit.

For instance suppose one generate a rectangular mesh. Then my question is how much smaller in practical terms is the size of the single rectangle. It could be in pixeles, centimeter or any appropriate unit.

Alammar May 23, 2002 05:23

Re: size of element
Given the limited resource than one has, the best grid size would be that which is enough to attain grid independance. However, when you speak of the smallest possible, one need to remember that the governing equations are applied at each cell. This cell, then, can not be smaller than allowed by the continuum hypothesis.

Alammar May 23, 2002 11:25

Re: size of element
I must try and challenge myself on my previous statments. An engineer first wears his/her "engineering hat" and then correctly argues that the contnuum hypothesis is satisfied by the scale he/she is working on. The engineer then happily applies the boundary conditions to his governing equations. Now, the engineer reaches out for his back pack and grabs on his/her "mathematician hat" and forgets his/her engineering background. He/she then applies finite difference, proving with Taylor Series that the smaller the grid size, the closer the solution would be to the exact. No limits. No continuum. I may be able to say that finite volume can be a bit confusing if one is not careful! Thanks Solomom for your question! I hope I'm right this time!

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