[[mesh]]

Due to the small aspect ratio of ice-sheets, but also glaciers, creating a mesh for a glacier geometry or an ice-sheet geometry cannot generally be done using classical meshers. Our experience in modelling different glaciers, ice-caps and ice-sheets, is that a vertically structured mesh is very often the best solution. Such a mesh can be constructed by first meshing the footprint of the glacier contour and then extruding this footprint vertically. The extrusion can be done either before running the simulation or using the internal mesh extrusion feature in Elmer, as presented below.

This Section presents some tools that have been developed and are used to construct a mesh for a glacier type geometry.

The characteristics of these different tools are listed in the following tabular:

Tool | DIM | Initial Mesh | Data (bed and surface) | Interpolation |
---|---|---|---|---|

MshGlacier | 2D | 2D square 1×1 | (x,z) points | linear / cubic spline |

ExtrudeMesh ^{1)} | 3D | 2D footprint | (x,y,z) points^{2)} | `1/r^m` inverse distance approximation |

MshGlacierDEM | 3D | 3D footprint x 1m | DEMs | bilinear |

MshGlacierSynthetic | 2D & 3D | 2D or 3D footprint x 1m | functions | N/A |

^{1)} possibility to include boundary layer at top or bottom
^{2)} randomly distributed supporting points

Other usefull tools for mesh generation are GMSH, a three-dimensional finite element mesh generator and the fully automatic adaptive isotropic surface remeshing tool YAMS .

Meshing tools to create the mesh of a 2D domain from a closed contour are available here.

The contour can be given as a shapefile. The elmer mesh (elements and boundary elements) can be converted to shapefiles to be visualised in a GIS software (e.g. QGIS).

Elmer proposes special solvers to perform efficient mesh and variables manipulations when the mesh is structured. Elmer also allows to perform internal extrusion during the simulation to create such structured mesh from a 2D-footprint. These features for structured meshes are documented here. The material course presented in April 2013 at Edmonton takes into account some of these features. More information can also be found in the Elmer documentation.

Many problems require to have a high mesh resolution in some particular locations (e.g. close to the grounding line, to capture few-kms-width ice-streams in large-scale ice-sheet simulations etc…, see e.g. Gillet-Chaulet et al., 2012). Having a fine mesh resolution everywhere in the model domain is often not computationnally affordable. Adaptive mesh refinement (AMR) is a method where the accuracy of the solution is controlled by spatially adapting the mesh size. The main difficulty is to find efficient and reliable estimators of the numerical error to control the mesh size.

Here, we use an error estimate based on the interpolation error, proposed by Frey and Alauzet (2005). Routines to compute the anisotropic metric defining the mesh size have been implemented as Elmer/Ice Solvers. The mesh adaptation is performed using the freely available library MMG (http://www.mmgtools.org, Dapogny et al., 2014).

Our implementation is actually restricted to the adaptation of plane-view 2D meshes comprised of linear 3-nodes triangular elements. This procedure was previously performed using external codes and the remeshing software Yams. The mesh adaptation features are documented here.