Spatial Domain

Visit Spatial Domain for detailed usage.

Interior Models (Optional)

Interior Models tag is used to state the behaviour of the region. The evolution equations of the models set in these tags are going to be executed for the region.

Initial Conditions (Optional)

Visit Initial Conditions for detailed usage.

Interactions

The combination of different regions with potentially different models raises the question of how to deal with the interface between regions. Simflowny allows different strategies:

• Surface models: for each region it is possible to define different models for the volume (interior) and the surface. This permits, for instance, a surface model defining fields that will be useful for neighbour regions. This characteristic is only available in Subregions
• Region interaction: it is possible to override the model of a region with static terms on the surface of contact with a specific regions.

The Region element can only have region interactions. Given a particular region, one may define a specific interaction with another region or boundary. In order to define such interactions, one must add a Interactions element using the region contextual menu. In particular, interactions consist of:

• The list of regions to interact with (Target Regions)
• The terms that overwrite the model equations in the region interaction interface. The terms defined in the interaction will be applied to all the fields in the region regardless of the information propagation speed and the orientation of the interaction surface.

There are three king of interactions: Field Interaction, Eigen Vector Interaction and a generic Interaction

When choosing Field Interaction, the terms defined in the interaction will be applied to all the fields in the region regardless of the information propagation speed and the orientation of the interaction surface.

With the Eigen Vector Interaction (to be used only if the associated models contain full general characteristic decomposition information), expressions will depend on an arbitrary unit vector, n = [nx , ny , nz], also tensors fields will be projected on transverse and along directions of vector n, and only such eigen vectors with incoming characteristic speed will be computed according to the region interaction expressions rather than to their regular expressions. In particular, what it is being done is to compute the predicted eigen vectors according to their regular expression, then to check for eigen vectors with incoming characteristic speeds and correct them according to the expressions defined in the region interaction and, finally, use the undiagonalization expressions to recover the evolution fields.

Choosing Interaction, expressions are defined similarly as it is made for the evolution equations. Please, go to evolution equations section in the PDE Model User Guide for a detailed explanation of how to define the terms.

Even with all the options that users have to define region interactions, it is important to point out a common potential problem that could be found when dealing with incompatible regions; this is, regions making use of fields not defined in an adjacent region. The computation of derivatives in points close to the interphase will fail since it requires the evaluation of the fields in the neighbour points. Simflowny overcomes this problem by automatically detecting incompatible regions and performing an extrapolation of the missing fields. Currently, three extrapolation algorithms are supported, namely, Linear, Quadratic and Cubic spline (where the number of interior data points used in the extrapolation can be chosen by the user). This information is provided by the user in the discretization policy.

Below a picture of a projection for variable φ from am interaction:

Field groups (Optional)

Grouping fields can be useful for discretization schemes using different algorithms for different fields. Defining groups of fields in the regions enables the usage of these specific schemes. Check Discretization Policies for more detail.