Reg. the instability in pressures in HM problem

Dear OGS Team and Prof. @Thomas_Nagel

I am solving a coupled HM problem (up formulation) for slope stability analysis under fully saturated conditions with a load at the top of the slope crest. However, I am getting spurious oscillations in the pressure wave during my simulations (Figure attached). I learned that it is the typical incompressibility constraint for hydromechanically coupled problems as I do not meet the Ladyzhenskaya-Babuška- Brezzi (LBB) stability condition.

I found several ways to overcome this problem by using various stabilization methods (e.g., White and Borja, 2008). But the easiest way to eliminate the instability is by choosing a Q9P4 element (i.e., 9 nodded quad for displacement/4 noded quad for pressure).

I would like to know if there is any way of using the Q9P4 element in OGS for the HM problem. Also, I am open to knowing other possibilities for solving this numerical issue.


Hi Pavan. You’re right. Nice example of the instability, actually. We typically use Serendipity elements in OGS (Q8P4) for this. You have to convert your mesh to quadratic elements (there’s a tool in your bin folder for that, just ls for Quadratic). Don’t forget to also convert the boundary meshes along with that.

Then, you set the integration order to 3 in your input file and the order of the displacements in process variables to two, leaving pressure at one.


PS: simple example is here: Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2.prj · master · ogs / ogs · GitLab

Thank you very much for the prompt response, Prof. @Thomas_Nagel

It worked. The interpolated pressure seems continuous. However, the pressure (i.e., primary variable) still has the shocks. Similar observations were seen in the suggested example by you. As far as the representation of pressure contours is concerned, the interpolated pressures will do the job.

However, I think the oscillating pressure values still affect the mechanics through its coupling term because the mechanics’ module is coupled by the pressure but not with the interpolated pressure.

Also, I observed more significant oscillations in pressure while using Q8P4 elements than T3 elements. Moreover, the interpolated pressures are continuous for Q8P4 elements.

Any thoughts on this?


This is just a plotting artefact, as pressure does not formally exist in the edge-center nodes. So You have to plot interpolated pressure. If that’s fine, then your solution is fine.

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Now I get it. Thanks, Prof. Nagel.