2D Mesh Generation

FEFLOW 8.0 supports the generation of either triangular or quadrangular finite-element meshes. A separate panel is available to support the mesh generation process ( Meshing panel). The starting point of the 2D Mesh Generation is always a Supermesh. This will delimit the outer border of the 2D model domain, as well as all internal features such as point, lines or internal boundaries (e.g. inner polygons). The finite-element mesh generation is based on the input of an approximate number of finite elements to be generated, certain rules for mesh local mesh refinement and desired mesh density of each supermesh polygon.

Different algorithms for the mesh generation are provided, all of them with their specific options and properties. Some algorithms can consider also lines and points in the supermesh and allow a local mesh refinement at polygon edges, lines and points.

Mesh generation is typically a trial-and-error process. The user hereby iteratively optimizes element numbers, generator property settings and—if necessary—the supermesh until a satisfactory mesh is obtained.

Significant effort can be involved in mesh generation, especially in cases with a large number of geometrical constraints (many polygons, lines and points). In typical cases, however, the effort required for generating a good finite-element mesh saves time at later stages of the modeling process due to reduced risk of instabilities.

Specific details about the mesh generation are described in next section 2D Mesh Generation Workflow.

Mesh Generation Algorithms 2D

There are many different strategies for the discretization of complex domains into triangles and quad elements in 2D. As each has its specific advantages and disadvantages, FEFLOW supports three different algorithms for triangulation and one for quad meshing. As a further step in the flexibility of model construction, FEFLOW 8.0 has the ability to Quadrangulate (Refine) the Full Triangular Mesh or Convert to Quad/Hex-Dominant Mesh. Both options are available via the Mesh menu.

Advancing Front

Advancing Front is a relatively simple triangular meshing algorithm that does not support any lines or points in the supermesh. If present, they are simply ignored in the generation process. Its main advantages are its speed and its ability to produce very regularly shaped elements.

GridBuilder

GridBuilder—developed by Rob McLaren at the University of Waterloo, Canada—is a flexible triangulation algorithm. GridBuilder supports polygons, lines and points in the supermesh as well as mesh refinement at points, lines, or supermesh polygon edges.

Triangle

Triangle is a triangulation code developed by Jonathan Shewchuk at UC Berkeley, USA. It is extremely fast, supports very complex combinations of polygons, lines and points in the supermesh, allows a minimum angle to be specified for all finite elements to be created, and provides the means for local mesh refinement with a maximum element size at lines or points of the supermesh.

Transport Mapping

Transport Mapping is the algorithm used for generating meshes of quadrilateral elements. This option requires that the quad meshing option in the Mesh menu is selected and that all supermesh polygons have exactly four nodes. Lines and points in the supermesh are ignored when generating quadrilateral meshes.

More details about each of the generator are discussed later in its specific section.

2D Mesh Editing

Some specific modifications of the finite-element mesh are possible at any time after mesh generation, even after model parametrization:

Deletion of elements
Mesh refinement by element subdivision
Mesh de-refinement (after previous refinement)
Splitting of quad elements into triangles
Splitting of triangular elements into quads
Convert triangular mesh to quad-dominant mesh
Smoothing of the mesh at selected node locations or of the entire mesh
Flipping element edges (triangular elements)
Moving nodes within the area of the surrounding elements

All the mesh-editing functionality is contained in the Mesh-Geometry toolbar or in the Mesh menu.