Basic data

The basic data covers all that can be considered variables in a PDE problem or model. There are eight elements:

• Fields.
• Coordinates.
• Auxiliary fields (optional).
• Analysis variables (optional) (only in problems).
• Auxiliary variables (optional).
• Eigen vectors (optional) (only in problems).
• Tensors (optional)
• Parameters (optional).

Now there is the explanation of the element meaning:

• Fields: these are the physical fields you want in your problem. For instance: the 3 components of the magnetic field, a density field, components of the velocity field, pressure, etc. Notice that the name of each field must be unique, and the system does not distinguish capital standard alphabet letters and lower letters (this is, E and e are the same field). However, φ and Φ are different fields.
• Coordinates: this is where you define the main coordinate system in your problem. Typically, if you use a Cartesian coordinate system you will choose x, y, and z if your problem involves a 3D scenario for spatial coordinates. Notice though that any name is valid. You can have 1 to 3 spatial coordinates. The time coordinate is compulsory as Simflowny supports transient problems, not equilibrium problems (you may have noticed we did not mention elliptic problems). Notice also that you can only have one time coordinate.
• Auxiliary fields: these are extra fields you may want to include as a way to simplify expressions in the problem, monitor stability, accuracy, or provide some simplified views on the simulation status. These fields are not associated to an evolution equation (i.e., no PDE equation for the time derivative of the field may be defined), but rather are bound to other fields through algebraic expressions.
• Analysis variables: these are variables used exclusively to output a quantitative analysis from the evolution. Analysis variables do not evolute in time. Furthermore, the calculations of the analysis variables are only performed when they are going to be writen to disk. Despite depending on model variables, analysis is defined in problems because they are specific to concrete domains. For instance, the analysis of the existence of gravitational waves in a black hole collision is specific to the problem setting; the Einstein equations should not define that analysis since they can be applied to problems without blackholes.
• Auxiliary variables: these are extra variables you may want to include as a way to simplify expressions in the problem, monitor stability, accuracy, or provide some simplified views on the simulation status. These variables are different from auxiliary fields in two ways, they allow derivative terms, just like evolution equations. The second difference is that these variables are not stored in memory, but they are computed locally and then disposed.
• Eigen vectors: when a problem contains more than one model having eigen vectos in their characteristic decomposition, it is possible that their names are repeated. In that case, as they refer to diferent diagonalizations, it is necessary to univocally identify each eigen vector from the models. This tag must be filled and then eigen vector equivalence in the model tag must be filled too.
• Tensors: usually fields in Simflowny are given component by component, since the information must be scalar. Nevertheless, for characteristic decomposition, information about problem tensors is useful to get normals and traverses from those tensors. For instance, a first order tensor m composed by mx and my in a 2D problem allows the usage of m_n, m_tx and m_ty variables in diagonalization and undiagonalization in characteristic decomposition.
• Parameters: frequently your problem will depend on different parameters which you cannot or do not wish to define at this stage. Typically you will run your simulation changing these parameters by hand from a configuration file. It is possible to set a default value for a parameter in order to be a reference for a user of the problem. The Reynolds number or the speed of light in a material are examples of parameters.

The following picture shows an example of a 2D Wave Equation problem basic information: