This 3D glacier model combines Stokes momentum balance and coupled, implicitly-computed ice geometry evolution using the surface kinematical equation. Arbitrary ice geometry and topology changes are allowed as the problem is regarded as a fluid layer evolution subject to a nonnegative thickness inequality constraint (Bueler, 2020). Conservation of energy, sliding, floating ice, and bedrock motion are not modeled. The numerical method uses Q2 x Q1 (velocity x pressure) finite elements on a 2D or 3D extruded mesh. A vertical displacement field is solved-for simultaneously with the Stokes equations; this also uses a Q1 element.

The current project includes a draft paper simp.tex in paper/ and Python programs in py/.

These programs use Firedrake, and thus PETSc under the hood (Bueler, 2021). A brief introduction is in py/README.md

See the references cited in simp.tex. In addition, an earlier Firedrake Stokes model with explicitly-updated geometry appears in my McCarthy Summer School notes repository mccarthy/stokes/.

• E. Bueler, Conservation laws for free-boundary fluid layers, 2020, arxiv:2007.05625