[Knowledge]

Hi guys

I have to do a mesh independency study. What makes it difficult is that it is not steady-state mode, but transient. Is it enough to compare e.g. three time-points for each mesh and thereby determine the mesh independency? Or what is the most common approach?

Thanks!

[karachun]

Yes, based on 3 points you can make extrapolation (Richardson's extrapolation) and determine the result "at infinity" and determine how far is your result from the "ideal" result.
Here is a link to an article.
https://www.grc.nasa.gov/www/wind/va.../spatconv.html

[ghorrocks]

Alexander, Richardson Extrapolation is for 3 different mesh sizes so you can extrapolate to zero mesh size (the theoretical ideal mesh). I read Sara's request as she has 3 time points in a transient simulation she is interested in, so Richardson extrapolation is not relevant for this.

Sara: mesh independency checks should be done on a parameter which is important for what you are trying to do. If the value of a variable at those three time points is important to you then yes, this is a good approach. If the time average is more important then you should use that, or if the period of the flow oscillation is important then you should use that. Whatever is important to you.

The concept of mesh independency is very similar in steady state and transient simulations.

[Knowledge]

Originally Posted by ghorrocks

Alexander, Richardson Extrapolation is for 3 different mesh sizes so you can extrapolate to zero mesh size (the theoretical ideal mesh). I read Sara's request as she has 3 time points in a transient simulation she is interested in, so Richardson extrapolation is not relevant for this.

Sara: mesh independency checks should be done on a parameter which is important for what you are trying to do. If the value of a variable at those three time points is important to you then yes, this is a good approach. If the time average is more important then you should use that, or if the period of the flow oscillation is important then you should use that. Whatever is important to you.

The concept of mesh independency is very similar in steady state and transient simulations.

Would it then be fine to look at e.g. three time-point for each mesh-size e.g. 6 different mesh-sizes and then observe if there is a difference between the mesh-sizes based on the parameter-values for three-time points obtained for each mesh-size? Can you recommend me an article?

[Knowledge]

Originally Posted by karachun

Yes, based on 3 points you can make extrapolation (Richardson's extrapolation) and determine the result "at infinity" and determine how far is your result from the "ideal" result.
Here is a link to an article.
https://www.grc.nasa.gov/www/wind/va.../spatconv.html

Can I use Richardson's extrapolation when I have transiet-mode? Maybe it's better just to choose one time-point for each mesh-size? And then I should just choose to look into three mesh-sizes e.g. coarse, medium and fine? And if I whish I can do it for several other time-points.

[ghorrocks]

You can use Richardson Extrapolation to approximate the ideal mesh and the ideal time step size. But I would do both as separate exercises. If you are trying to do both at the same time then I will refer you back to the derivation of Richardson Extrapolation and you can work out the maths for yourself.

To answer your question, yes, you can use Richardson Extrapolation for transient simulations. A good way to do this is to select an important parameter at a specific time point on all the different mesh resolution simulations, and do Richardson Extrapolation on that.

The classic text on CFD accuracy is "Computational Fluid Dynamics" by Roache. He did al lot of the fundamental work in defining how accurate CFD simulations are.