The influence of mesh resolution

[jlikermanUPC]

Dear UW team,

We are doing some tests with a 2D thrust wedge model and we realized that the evolution of the model changes drastically as the resolution increases after a threshold (512 for the x-axis).

We understand that the selection of the resolution is a sensitive issue, but what explanation can be given to obtain such different models? By increasing the resolution of the regular mesh, and therefore the amount of swarm particles, does that make the model subject to small stress perturbations and therefore result in the development of more structures? Additionally, non-rectangular cells can influence this behavior?

Figure 1: 512x128

Figure 2: 1024x128

We're using Underworld2.13

Thanks,

Jeremías

[tingyang2004]

The mesh size affects the strain rate, and because plasticity (and maybe dislocation creep) is considered in your model, the result is expected to depend on the resolution. However, I doubt that mesh resolution alone can cause such a significant difference in the model’s evolution. Maybe the initial weak seed or other physical parameters depend on the mesh resolution in your model? Also, is the dimensional time the same between these two models?

[jlikermanUPC]

Hi @tingyang2004 , thanks for the reply.

Ok, that makes sense but the difference remains substantial.

The initial weak seed is a velocity discontinuity located in the bottom center of the model. Yes, the dimensional time is the same in both models.

[tingyang2004]

Are you saying that the horizontal velocity of the base boundary is imposed as a Dirichlet boundary condition, and that the imposed velocity is discontinuous at the horizontal center? In this case, the physical model of the weak seed setup does not depend on resolution, but maybe the inhomogeneity introduced by your initial weak seed may have effects lower than or comparable to that of the random error (e.g., introduced by the swarm whose initial position is usually randomly assigned). In this case, rerun the model at the same resolution may also make a noticeable difference.

[julesghub]

@jlikermanUPC it would be good to see the high res. "regular" results, ie, 1024 x 256, 2048x512, ....
Perhaps the model was initially underesolved in the vertical direction with 128.
Also solver tolerances could impact the results of fine (and finer) shear banding.
Maybe decrease (tighten) the tolerances for high resolution if you still observe different outcomes at difference resolutions.

[jlikermanUPC]

@tingyang2004, indeed, the issue we are facing does not seem to originate from the generation of the weakness seed itself, but rather from the overall result of the model. In fact, failure occurs consistently in the seed's location in all runs. On the other hand, we have run several models keeping the resolution (either the same or varying it minimally) and there are not substantial changes.

Thanks @julesghub, we will carry out the suggested tests. Currently, we are running mumps solver with a tolerance of 1e-2. Would you recommend reducing it to 1e-3?

[bknight1]

I agree with @tingyang2004 initial comment and @julesghub comment on the model being under resolved in the vertical direction.

To me, this looks similar to the 'wide' and 'narrow' rift phenomenon, which is dictated by the viscosity at the base of the crust. As your resolution increases it looks like the viscosity at the base of the crust appears to decrease. This is probably due to the higher resolution capturing the change from strong plastic crust to weak viscous crust below the brittle-ductile transition. The weaker the lower crust the more spread out (or wider) the deformation becomes. This may be why you see it after a certain resolution, I assume the models before this critical resolution look like fig 1 and all modes after look like fig 2.

[jlikermanUPC]

Thanks to all, we conducted the test and found the best mesh resolution.