The 3D Supermesh

The 3D Supermesh is intended for re-using existing geometrical information to build a 3D finite-element mesh, e.g. a geological model can be taken as an initial point for the construction of the 3D Supermesh and subsequently finite-element mesh.

Before meshing the domain, the imported geometries are converted into a 3D supermesh. The workflow is supported by the New problem wizard. Addi¬≠tional elements can be added directly to the Meshing panel if needed, before continuing with the meshing process. Other than 2D Supermeshes, the 3D supermeshes also allow to retain certain information contained in the map data for the final mesh. For example, regions can be marked for later grouping of elements. This functionality is essential as it will facilitate the model parametrization in a later stage.

Piecewise Linear Complex

The 3D FEFLOW Supermesh is built following the concept of a Piecewise Linear Complex (PLC) from TetGen. A PLC describes a 3D geometry by a set of 3D elements (or 3D polygonal regions), each element is properly described by a set of vertices, segment and faces. Each element of the PLC must be closed under intersection. For example, two segments can only intersect at a common vertex. Two facets may intersect only at a shared segment or vertex or a union of shared segments and vertices (because facets are non-convex). Below we show two examples of non-closed configurations for a PLC.

The concept of a Piecewise Linear Complex (PLC). Image has been adapted from TetGen Manual.

 

The input geometries have to fulfil strictly the concept of a Piecewise Linear Complex (PLC). In practical words, this means no gaps or overlaps are allowed in surfaces describing the meshed domains, and no intersections may occur in any of the supermesh elements. A common error in the input geometry is that a line add-ins may not intersect at any surfaces or the boundary of the model domain, i.e. the intersection point is not prescribed in both line and surface geometries.

In case the requirements are not fulfilled, the mesh generation will result in an error message saying that the input geometries have self intersections.

 

The PLC definition is automatically created based on the map file (s) imported via the New FEM Model wizard in FEFLOW. Below it is shown an example of a PLC built using a geological input file. Here we can clearly observe the internal definition of the facets, which represent the geological contacts between neighboring units (or regions, volumes).

 

Example of a Piecewise Linear Complex built from a geological model.

Further details about the creation of 3D Supermesh in FEFLOW are discussed in section 3D Supermesh Design Workflow.

3D Supermesh Elements

A FEFLOW 3D Supermesh is built based on a set of surfaces, segments and vertices. Currently version of FEFLOW does not support the edition of a 3D Supermesh. If the model conceptualization requires to be adjusted, the modification (s) will have to take place in the input map files before these are imported for the 3D Supermesh.

Surfaces

Polygon maps are loaded as surfaces. They define the 3D boundaries of model regions. While general polygon maps are basically supported, it is for most applications highly recommended to use triangulated surfaces for this purpose.

Surfaces used for the construction of a 3D Supermesh can have their own Facets Area Constraints, which will provide additional information for further refinement during the meshing process. Moreover, these 3D polygonal feature can be grouped based on their name or attributes to allow the further creation of face selections.

 

It is highly recommended to prepare the input map files in a manner that the automatic creation of FEFLOW selection sets can be achieved. Such as workflow will facilitate tremendous the assignment of material properties in a later stage.

For example, a common approach case if the 3D Supermesh is built based on a 3D geological model, is to make a distinction between surfaces, which define the geological contact in respect to faults / fractures. Such as distinction can be simply done by using a different ID (or name) in one of the attribute of the input file. This will help later to have ready face selections for creating Discrete Feature Elements in the case of the faults / fractures or even to provide a different refinement level to these surfaces (Facets Area Constraints) if desired.

Lines

Lineal features can be imported using the New FEM Model wizard to build the 3D Supermesh. Following the principle of a PLC, the line feature should be properly described in the input geometry in such as manner self intersection is not produced. The wizard provides the possibility to group the line features following certain names or attributes, this will allow subsequently the automatic creation of edge selections.

Points

Point map files can be used as Add-ins to define new nodes of the finite-element mesh, or to preserve certain regions as selection sets or to delete certain regions after the mesh has been generated.

  • Region markers can also be used to constrain the element size for the region, e.g., by using an attribute of the marker point in the map.
  • Hole markers can be used to indicate that a specific region in between the surrounding surfaces is a hole in the domain and is not to be meshed.
  • Add-ins are used to pass certain number of new nodes to the resulting finite-element mesh. A typical application is for the definition of well boundary conditions.
  • Custom points can be split up into different kind of markers by using an attribute column in the imported map file.

Example of 3D Supermesh and an elemental selection preserved after the meshing process by using Region markers.

Analog to the case of surfaces and line features, additional details about the workflow with 3D Supermeshes is discussed in section 3D Supermesh Design.

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