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Tuesday May 28, 2019 at 11:43am

Let’s start by explaining the more straightforward to achieve of the two - convergence.

As a steady state flow simulation progresses through its iterations we can see if parameters of interest (goals) reach constant values (converge). Flow automatically sets criteria (which can be overridden) to make sure these goals have reached that constant state. Once they have then the solver will stop, this is controlled on the finishing tab of calculation control options. If our goals are truly converged, then running through more iterations isn’t going to give us a different solution.It is tempting to say that we have reached a good solution at this point however this isn’t the full story.

We can get a converged solution from a coarse mesh and a completely different converged solution for the same study using a fine mesh. Convergence alone doesn’t tell us we’ve reached a good solution - we need to do a bit more work here.

With any simulation study we’re looking to find that Goldilocks value where refining the mesh further doesn’t give a more accurate result. We can then run further studies using this mesh to get accurate solutions from minimal time and computational effort. This is a really useful place to be when running multiple scenarios of the same study. Getting to this point normally requires a mesh independence test where we vary the number of elements and see how this effects a parameter of interest.

*Below shows the plot you could expect to see.*

Now what if I told you that you can ensure convergence and mesh independence in SOLIDWORKS Flow Simulation in just one study AND refine the mesh where the refinement’s needed most? Pretty neat right?

To do this we need to dive into the often overlooked ‘refinement’ tab on calculation control options. Here we can set options for performing mesh refinement mid calculation at locations the solver thinks are best. I’m using the simple Coletor from lesson 1 of the Flow Simulation course as an example. This is a fairly typical internal flow problem, with a single inlet splitting to multiple outlets. A good solution here would show converged and mesh independent values for outlet volumetric flow rates – so those we’ll monitor these using goals.

The refinement strategy tells the software when to perform a mesh refinement; setting this to goal convergence means the mesh will be refined once our goals have converged. Goals can be selected from those created; in this example I’ve selected all of them. It’s useful to add a delay after convergence to ensure goals have absolutely converged before the next mesh refinement starts. On a similar note a relaxation interval of iterations after the final mesh refinement can be set to ensure the solution has run for long enough to fully converge. Here I’ve set a delay of 20 iterations and a relaxation interval of 50 (though these will vary study to study). Importantly on the finishing tab we can set the number of refinements to complete before the solution ends. We’ll want to make sure we’ve set the maximum refinement number and refinement level to at least this value. Here I’ve selected 5 for all three values. If there were any local mesh refinements these could also be controlled here.

So, what results can we get from this? Starting the study with a coarse mesh we see our goal values converging, once these converge the mesh refines itself. This refined mesh has a different converged solution to the coarser mesh so we see goal values changing and converging on new values. Once fully converged the mesh is refined again until the number of refinements specified has been reached. Here we see how the values for a parameter of interest (in this case one of the outlet volume flows) varies as the solution progresses. I’ve highlighted when the mesh is refined, pretty cool to see what’s going on!

Not only does SOLIDWORKS Flow refine the mesh, it also does so only at specific areas. How does it do this? Helpfully, the software looks for high pressure and velocity gradients where averaged values across the cells of a coarse mesh would give a poor result. Refining here ensures these high gradients are accurately captured. Here we can see the stages as the mesh is refined at the inlet (coloured by velocity), notice that there’s a coarser mesh where there’s no significant velocity gradient – smart right?

*Note: Velocity colour not to scale.*

When running a mesh independence study manually we would then go through and extract the number of elements in each mesh and corresponding converged goal values to plot. Doing this process within one study Flow can produce a ‘refinement table’. With a little bit of post processing we can plot converged goal values for each mesh against the number of elements to get a mesh convergence plot. This makes it nice and easy to see the best mesh to use going forward. Alternatively, if we haven’t reached a mesh independent solution, we can increase the maximum global level of refinement and continue the study. In this case it can be seen that we reach within 2 % of our final solution value at mesh number 4, roughly 500000 elements (note the log scale on this chart). If we were running future studies this is the one we would use going forwards.

Next time you’re running a Flow Simulation try using the auto-refinement options. You’ll be surprised how easy it can be to find that sweet spot of a quick yet accurate solution!

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