How much mesh refinement should I do?

  • Last Post 09 May 2018
peteroznewman posted this 12 November 2017

 A linear statics model calculates a maximum equivalent stress, which is compared with a yield strength.

An initial mesh has a certain element size around the point of maximum stress. 
A second mesh with smaller elements is solved and gives a new value of maximum stress.
A third mesh with even smaller elements gives a third value of maximum stress.

How do you decide when to stop refining? 

One method is described in ASME V&V10.1 “Illustration on V&V for Computational Solid Mechanics” and is called Calculation Verification, one small part of the entire Verification and Validation process.

 Below is an example using a tetrahedral mesh with a Sizing Mesh Control on a Sphere of Influence.

Maximum Stress from six mesh sizes were plotted. The red line is a best fit line through the three smallest element sizes. This line, or the calculation in Section 7.2 of V&V10.1, can be used to extrapolate the maximum stress to a zero-size element. This is the estimate for the exact maximum stress, but is only valid when the results are being calculated in the asymptotic convergence regime. The line estimates the maximum stress is 607 MPa.  See this discussion for an alternative mesh control using inflation.

The three largest element sizes are clearly trending toward a very different zero-size element value and should not be used since those results are not in the asymptotic convergence regime. V&V10.1 has more information on how to determine if you are in that regime.

In this example, I used a factor of 1.5 to change each successive element size. V&V10.1 recommends the factor be > 1.3.

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Rashi posted this 09 May 2018

Thank you very much for this article.

In your article and in the V&V10.1 it mentions about "asymptotic convergence regime", how can we know our results are in this region?

The explanation in the standard is bit confusing (V&V10.1). Which compares a theoretical and a calculated value for variable"p".  


peteroznewman posted this 09 May 2018

Great question Rashi, and one that I had also pondered after finding the illustration and the standard to be lacking in clarity on that point.

Here is a tutorial that someone at NASA put together for CFD models. It has a paragraph on Asymptotic Range of Convergence.