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Dependance of wallShearStress on mesh parameters

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Old   October 19, 2020, 11:59
Default Dependance of wallShearStress on mesh parameters
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Guillaume Herment
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Hello everyone,

I started using openfoam recently in order to model the fluidic environment around a (biological) cell trapped in a microfluidic chip. We will soon have to deal with a lot of input data and a lot of simulations, so I'm trying to reach a high level of automation. I already have the model of the chip that I can use to determine the pressure and velocity field within a chip containing no cell. To do this I use the simpleFoam solver with no turbulence model and specify a volumetric fluid flow at the inlet. For each experiment we are conducting we can model the cell in 3D since we're using a confocal microscope. I can then concatenate the chip stl file with the cell stl file, convert the whole thing to fms and use cfMesh to mesh the whole thing. I usually use a cartesian mesh.

The parameter that I want to extract is the wall shear stress at the boundary of the cell, which can be done rather easily since the cell has its own defined boundary of type wall. I'm using the wallShearStress post-processing utility to determine the kinematic shear stress at the boundary.

I'm willing to minimize the time it takes to run a simulation by finding the coarser mesh that still gives me the right result. I ran around 60 simulations using the same (biological) cell model with different values given in meshDict, modifying the minimum (mesh) cell size, the maximum cell size and the value of the local refinement around the (biological) cell. Some did not converge but most did.

Once I have computed the shear stress on the whole boundary, I compute its average value for each simulation. I got a very interesting result, as most of them converged towards a given value of shear stress (wss1) while about a quarter of them converged towards another value that is around 30% lower (wss2). I took care of letting enough iterations for these values to be the actual final one so I'm pretty sure the problem doesn't come from there.

There is no straightforward common points between the 2 sets of simulation, but still I noticed that all the uniform meshes (min cell size=max cell size) converged towards wss1. Some very similar parameters could lead to different output values, for example using min=2um, max=4um, local=2um will lead to wss1 while min=2um, max=3um, local=2um will lead to wss2.

The are differences in the velocity field between simulations, but I can't pinpoint the point of the geometry that led to the discrepancy I've described. By using the plotoverline utility of paraview I can see that there are slight differences in the gradient of velocity surrounding the cell, but of the order of 1-2% at the points I looked at.

Does anyone have an idea of what can cause such a behavior, and how I can try to debug it ?

Thanks for your help, let me know if I wasn't clear in my explanations.
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