[WIP] Anisotropic mesh adaptation part 1: feature-based metric tensor

[bmunguia]

Proposed Changes

This PR is part of a joint effort with Alberto Perlini (@xla27) and Andrea Rausa (@rois1995) to implement anisotropic mesh adaptation in SU2. In our SU2 conference talks this year, I presented updates to the metric tensor computation in my fork for unsteady adaptation, and Alberto presented updates to the Python adaptation loop to use the open-source MMG remesher, as well as results for incompressible Euler/NS and NEMO.

Part 1 will focus on my contributions in SU2's post-processing/output to calculate metric tensor fields for feature-based adaptation. Part 2 will focus on the implementation of the adaptation loop in Python, including conversion between SU2 restarts/meshes and the .meshb format.

For the metric tensor field computation, I have implemented:

• CVariable containers to store adaptation sensor variable/gradient/Hessian/metric tensor
  • We only store the lower-triangular elements of the Hessian/metric, so the size of the array at each point is $nSymMat = 3*(nDim-1)$
• CSolver function SetPrimitive_Adapt() to store the chosen adaptation sensor
• Green-Gauss Hessian calculation in computeGradientsGreenGauss.hpp which calculates the Hessian field for the chosen sensor and stores the lower triangle
• Integration of the Hessian (symmetric positive definite by construction) determinant and Lp-norm normalization (see references) in computeMetrics.hpp
• Integration of the Hessian field in time for unsteady adaptation
• Output of metric tensor for different flow solvers, and updates to Paraview XML filewriter to allow for proper parsing of symmetric tensors

The following relevant config options have been added:

• COMPUTE_METRIC (bool) - whether to calculate the sizing metric in post-processing (default False)
• NORMALIZE_METRIC (bool) - whether to perform the Lp-norm normalization of Hessians (default True)
• NUM_METHOD_HESS (str) - gradient method for Hessian calculation (only GG for now)
• METRIC_SENSOR (str) - field to use for sizing metric
• METRIC_NORM (unsigned short) - choice of norm for Lp-norm normalization
• METRIC_COMPLEXITY (unsigned long) - target mesh size
• METRIC_HMAX (float) - maximum cell size (constraint on minimum metric tensor eigenvalue)
• METRIC_HMIN (float) - minimum cell size (constraint on maximum metric tensor eigenvalue)
• METRIC_ARMAX (float) - maximum cell aspect ratio (constraint on ratio of hmax to hmin)

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

References

1. Loseille and Alauzet. “Continuous mesh framework part I: well-posed continuous interpolation error,” 2011.
2. Alauzet and Loseille. “A decade of progress on anisotropic mesh adaptation for computational fluid dynamics,” 2016.
3. Perlini. "Mesh adaptation in SU2: current status and perspectives," 2025.
4. Munguía. "Towards a deep learning framework for time-accurate anisotropic mesh adaptation," 2025.

[pcarruscag]

Is the mesh adaptation code itself open source?

[bmunguia]

If you mean MMG, it's on Github https://github.com/MmgTools/mmg

If you mean the SU2-MMG interface, it's in Alberto's fork https://github.com/xla27/SU2/tree/feat_adap_mmg

[pcarruscag]

Excellent. Next question, what do you need from the python wrapper to do all of this outside of the SU2 core?

[bmunguia]

The python script basically just coordinates calls to SU2 and MMG in 2 nested loops, the inner loop being a series of adaptations at a given target mesh size and the outer loop being over a list of sizes. It also handles file conversions since MMG uses libmeshb for both the mesh and metric field.

For the file conversion, Alberto has a straight python implementation that I think only handles tris/tets, and I have a separate repo with a C++ implementation/python API that I used for my results that I presented in Varenna https://github.com/bmunguia/limon

[pcarruscag]

Cool, the functionality would be more flexible if the sensor was also configurable via python, what you have here has a list of hardcoded possible variables, in python it would be very easy to target other solvers, create custom mixes of variables etc.
So maybe a helper to compute a generic gradient/hessian in c++?

[bigfooted]

Hi Brian, what's the status?

[bmunguia]

Hey Nijso, sorry for the delay. I've been a bit swamped lately with a deadline and the holidays so this has been on the backburner, but I'll look at it again this week or next. I know a lot of people have been asking about adaptation on slack so I want to get this in develop ASAP.

I still need to implement Pedro's suggestions to use the python wrapper to make the choice of metric sensor more flexible, then I just need to add an example (or maybe a few for different solvers) to test the implementation.