System Coupling supports multi-region coupling interfaces, where more than one region is specified per side. Generally, the preferred approach is to use one region per coupling interface - that is, to agglomerate multiple topological regions into a single coupling region inside the participant solver. However, if agglomeration is not feasible, the implementation of the participant library APIs should be consistent with the rules described in this section.

Mesh Definition for Multi-Region Coupling Interfaces

When providing access to region mesh for a multi-region case, care should be taken when handling shared nodes. Shared nodes are nodes that are used in more than one region. Figure 1 illustrates this scenario. In this example, there are two surface regions defined, and each region has a simple mesh that consists of one quadrilateral element. Region L has 4 mesh nodes, as does Region R. However, when taken together, there are only 6 unique nodes between these two regions, because the 2 nodes in the middle (marked A and B) are shared nodes.

Figure 1: Example of two regions with shared mesh nodes

System Coupling will detect a shared node by its node id. For example, if node A is given an id of 4 when defining the mesh for Region L and the same id of 4 when defining mesh for the Region R, then System Coupling will interpret the node A as shared between the two regions. To further illustrate this example, surface mesh arrays for both regions are shown in Figure 2.

Figure 2: Mesh arrays for the case with shared nodes

As shown in Figure 2, nodes with ids 3 and 4 are repeated in the definitions of both regions. From the above example, it is obvious that some redundant information is provided for shared nodes — node coordinates are provided multiple times, once for each shared node for each region. For a given shared node, System Coupling will use only one set of coordinates (from one of the regions) and will disregard all others. Therefore, it is critical that nodal coordinates for shared nodes are identical.

To contrast the case with shared nodes and the case without shared nodes, compare Figure 2 to Figure 3. The latter figure shows the case without shared nodes. Note that this is a different setup and may result in a different solution.

Figure 3: Mesh arrays for the case with non-shared nodes

Finally, these two regions can be agglomerated into a single region, as shown in Figure 4. If the two regions above are to be used in a single coupling interface, then agglomeration is preferred but not necessary.

Figure 4: Mesh arrays for the case where regions are agglomerated into one

Solution Field Data for Multi-Region Coupling Interfaces

When working with multi-region cases, one should also be careful with how the solution field data is handled on shared nodes. If solution data is defined on mesh nodes, then different treatment is required, depending on whether the variable is extensive or not.

Values for extensive variables are accumulated on shared nodes by System Coupling. Figure 5 shows an example of a extensive nodal variable (heat rate) for two regions, where each region consists of one quadrilateral mesh face (see previous section for how to define the mesh for this example). Nodes A and B are shared between these two regions. Note that in Region L, nodes A and B each have heat rate value of 2 Watts. In Region R, nodes A and B each have heat rate values of 3 Watts. Since heat rate is an extensive variable, the values on shared nodes will be accumulated. Therefore, when both regions are taken together, the shared nodes A and B will each have heat rate value of 5 Watts. The sum of heat rate values for both regions in this example is 30 Watts.

Figure 5: Nodal extensive variable (heat rate) values for the multi-region case with shared nodes

Values for intensive variables should be identical on shared nodes. Figure 6 shows an example of intensive nodal variable (temperature) for the same two regions as in the previous example. Note that shared nodes A and B each have identical temperature values in both Region L and Region R. To get the average temperature on these two regions, the sum of temperature nodal values is divided by the number of unique nodes. In this example, the average temperature is \((500 + 300 + 800 + 600 + 500 + 300) / 6 = 500 [K]\).

Figure 6: Nodal intensive variable (temperature) values for the multi-region case with shared nodes

NOTE: Sometimes, variable values on shared nodes can differ. For example, a shared node can exist between a region that represents fluid flow inlet and a region that represents a non-slip wall. In this situation, fluid flow velocity on the "inlet" node could be non-zero, while on the "wall" node, the velocity will be zero. However, in these situations, one would not want to include both these regions in a single coupling interface. If multiple regions with shared nodes are included in one coupling interface, then the intensive variable values on those shared nodes should be identical.