Submeshes for Boundary Conditions, Source Terms, and Flux Calculations

Motivation

Boundary conditions are defined on the boundary of a given domain. Source terms may exist on subdomains of the domain. Sometimes the flux across a subdomain is interesting for the modeller.

Consequently, we need a way to specify such subdomains for the Finite Element simulation. There are several possibilities to define a subdomain. One possibility is to use a geometry via a .gli- or .gml-file. Since the geometry often doesn’t match exactly on the domain mesh, one has to specify a search radius to find nodes, elements, or faces in the neighborhood of the geometry. It can be difficult to find an appropriate search radius for adaptive refined domain meshes. Finally, with the geometry and a suitable search radius the associated domain elements and domain nodes are searched for. Since this happens during the simulation, this approach is not very robust.

Another possibility, avoiding the search during the simulation and thus more robust, is to precompute the subdomains as meshes. These precomputed subdomains are now passed to the OGS-6 simulator in the same format as the bulk mesh, the VTU format. The subdomains additionally contain information to identify the corresponding bulk mesh entities like nodes, elements and faces of elements.

A simple example

In the next figures it is explained how a boundary condition can be set to the top surface of a quad domain for a OGS-6 simulation. The first figure depicts the bulk mesh and the id’s of the nodes on the top. The differently coloured top surface mesh can be obtained for instance by the ExtractSurface tool. For visualisation purposes the top surface is translated upwards. The picture shows the bulk mesh and the id’s of the nodes on the top of it. Furthermore, the translated top surface mesh with the corresponding bulk node id’s are represented.