Scope

Discretization schema

Usage

The content of the tag is the variable in which the auxiliary equations will be based.

Example

In this case, the auxiliary equations will use a specific shared variable.

Scope

Discretization schema

Usage

The content of the tag is the variable in which the conversion be based.

Example

Scope

Discretization schema

Usage

The typeAtt attribute indicates when the boundaries should be calculated with fluxes or fields. The two possible values are flux and field. This tag is optional, the default value is field.

The variable tag defines the variable in which the boundaries will be based.

The previousVariable is used to calculate some type of boundary conditions which requires the usage of the previous state of the variable.

The stencil tag specifies the width of the boundary in terms of cells.

Example

Scope

Discretization schemas.

Usage

The content of the tag is the variable in which the conditions variables will be based.

Example

In this example, the simulation will stop if the previous step of any field is greater than half of the two previous step of the same field.

Scope

Discretization schema (Inside math tags).

Infix

$flx

Usage

Fluxes are one of the components in which Simflowny decompose PDEs. When discretizing a problem, at a certain point, one want to get the flux information from the equations. For instance, to calculate centered differences one get the flux of the previous cell and subtract it to the flux of the next cell. In order to allow this calculations, the fluxes should be called within mathematical expressions.

Furthermore, fluxes can be expressions with different degrees of complexity. So, it is simpler to treat the fluxes as function calls. For instance:

One may call to the Flux \(F_x\), which uses the fields P, mx, my and ρ, but instead of using the fields directly, using a derivated fields P', mx', my' and ρ'. When writing a discretization schema, the writer does not know the quantity of fields needed by the flux, so instead of passing all of them as the arguments of the call, a base variable is used. Following the example,

Where u is a wildcard for any field.

As a consequence, the usage within a mathematical expression is like $flx(F$i$f, variable), where variable can be any variable and F$i$f is the way Simflowny identifies the flux function name.

Example

Flux_$i$f($cc) represents a group of variables called Flux with subindices representing all the combinations of spatial coordinates and fields. The $cc meaning currentCell indicates that the variable is asigned in the current cell. For instance, it could represents \(Flux_x\rho (i,j)\).

The left hand side of the equation represents a flux call ($flx(...)). The first parameter is the flux function name. The second one is the a variable to use inside the flux to represent the fields. For instance, it could represents \(\rho _eps(i,j)\).

Scope

Discretization schema (Inside math tags).

Infix

$sv

Usage

The $sv directive wrapping a variable indicates that the variable is considered as shared variable.

Example

The variable k1$f($cc) is considered a shared variable since it is inside the $sv directive.

Scope

Discretization schema (Inside math tags).

Infix

$fc

Usage

The $fc directive encloses the function name to call and all its parameters.

Example

This instruction will call a function with name weno and passes six more variables, defined previously.

Scope

Discretization schema (Inside math tags).

Infix

$src

Usage

The $src directive needs a variable to be used as a reference for the source's field replacements.

Example

The variable Sources_$f will store the sources for every field with the values for the field variable at the current time step. For example, if the sources of the current PDE are \(S^{(Bx)} = \left(-a\right)\mbox{ }{Bx}\), then the instruction would be \(Sources_Bx = \left(-a\right)\mbox{ }{Bx^n}\).

Scope

Discretization schema.

Usage

During the definition of the Characteristic Decomposition, in the model definiton, the user is required to introduce the coefficients of the (un)diagonalization expressions; this is, eigenvectors written as a linear combination of the evolution fields (or viceversa). Now here, the DSL can take advantage of this fact and use a different variable for the coefficients than for fields and eigenvectors. In particular: the variable parameter is the variable to be used for the fields of the diagonalization, as well as for the resulting eigenvector; the timeSlice parameter is the variable to be used for the fields in the coefficients of the linear combination.

Example

Scope

Discretization schema.

Usage

The variable parameter is the variable to be used for the eigenvectors of the undiagonalization, as well as for the resulting fields. The timeSlice parameter is the variable or timeSlice to be used for the fields in the coefficients of the linear combination.

Example

Scope

Discretization schema (Inside math tags).

Infix

$mcs, $pcs, $ncs

Usage

The $mcs, $pcs and $ncs directives need a variable to be used as a reference for the speed's field replacements.

Example

If the characteristic speeds would be \(c \ast u\), \(-c \ast u\) and \(0\), it would generate \(Speed(i) = max(c \ast u^n(i), -c \ast u^n(i), 0)\).

Scope

Discretization schema (Inside math tags).

Infix

$mcsc, $pcsc, $ncsc

Usage

The $mcsc, $pcsc, $ncsc directives need a variable to be used as a reference for the speed's field replacements.

Example

Imagine there are two spatial coordinates (x and y) with \(x + u\) as the speed in x, and \(y + u\) and \(y - u\) as speeds in y, being u a field. Then, the instructions generated would be \(Speedx(i) = x + u^n(i)\) and \(Speedy(i) = max(y + u^n(i), y - u^n(i))\).

Scope

Discretization schema (Inside math tags).

Infix

$cc

Usage

No parameters are needed.

Example

The previous picture shows an example of the currentCell usage. This mathematical expression represents a Forward Difference function, where the value would be the difference between the value for the variable in the next cell and the current one.

Scope

Discretization schema (Inside math tags).

Infix

$ic $dc

Usage

This tag requires the number of cells to increment or decrement from the current one. The parameter have to be added as sufix to the infix notation.

Example

The capture above shows the code for the centered differences function. The flux variable from the previous cell is subtracted to the value of the next cell (and divided by twice times delta x).

Scope

Discretization schema (Inside math tags). The math element including one of these tags must be within a parabolicTermsContext tag.

Infix

$ic2 $dc2

Usage

This tag requires the number of cells to increment or decrement from the current one. The parameter have to be added as sufix to the infix notation.

Example

Scope

Discretization schema (Inside math tags).

Infix

$icic $icdc $dcic $dcdc

Usage

This tag requires the number of cells (for the first and second coordinate) to increment or decrement from the current cell.

The parameters have to be added as sufixes to the infix notation.

If the first and second coordinate are the same for the current parabilc term combination, the first one is applied and the second one ignored.

Example

The image shows how theses tags are used to access indices for a crossed derivative.

Scope

Simml code (Inside math tags).

Infix

$sign

Usage

The $sign directive needs a variable to get sign from.

Example

The sign of p_a - p_b will be calculated.

Scope

Discretization schema (Inside math tags).

Infix

$pv

Usage

The $pv directive needs a variable to be used as a reference for the volume field replacements.

Example

The particle volume is calculated for the neighbour particle ($np).

Scope

Any section (Inside math tags).

Infix

$rffq

Usage

The number of parameters are variable, depending on the number of coordinates and variables to get, readFromFileQuintic(FileName, NCoords, NVars, CoordInputValue1, ..., OutputVar1, ..., VarIndex1, ...):

• FileName: name of the file to read from (without the .h5 extension).
• NCoords: number of coordinates in file.
• NVars: number of fields to read.
• CoordInputValues (Multiple): values for each coordinate to get position for interpolation of values (number of arguments must be NCoords).
• OutputVars (Multiple): variables to write output into (number of arguments must be NVars).
• VarIndices (Multiple): indices of the field datasets whose interpolations will be written into OutputVars (number of arguments must be NVars).

They can be used independent from the dimensionality of the problem. For instance, readFromFile1D can be used in a 3D problem. In that way, a user could map a radial initial condition from a 3D problem, calculating the corresponding radius of a cell and passing it to the function.

Scope

Any section (Inside math tags).

Infix

$rffl1d, $rffl2d or $rffl3d

Usage

The number of parameters are variable, depending on the number of coordinates and variables to get, readFromFileLinear(X)D(FileName, NCoords, NVars, CoordInputValue1, ..., OutputVar1, ..., VarIndex1, ...):

• FileName: name of the file to read from (without the .h5 extension).
• NCoords: number of coordinates in file.
• NVars: number of fields to read.
• CoordInputValues (Multiple): values for each coordinate to get position for interpolation of values (number of arguments must be NCoords).
• OutputVars (Multiple): variables to write output into (number of arguments must be NVars).
• VarIndices (Multiple): indices of the field datasets whose interpolations will be written into OutputVars (number of arguments must be NVars).

They can be used independent from the dimensionality of the problem. For instance, readFromFile1D can be used in a 3D problem. In that way, a user could map a radial initial condition from a 3D problem, calculating the corresponding radius of a cell and passing it to the function.

Scope

Any section (Inside math tags).

Infix

$rfflwd1d, $rfflwd2d or $rfflwd3d

Usage

The number of parameters are variable, depending on the number of coordinates and variables to get, readFromFileLinearWithDerivatives(X)D(FileName, NCoords, NVars, CoordInputValue1, ..., OutputVar1, ..., VarIndex1, ...):

• FileName: name of the file to read from (without the .h5 extension).
• NCoords: number of coordinates in file.
• NVars: number of fields to read.
• CoordInputValues (Multiple): values for each coordinate to get position for interpolation of values (number of arguments must be NCoords).
• OutputVars (Multiple): variables to write output into (number of arguments must be NVars).
• VarIndices (Multiple): indices of the field datasets whose interpolations will be written into OutputVars (number of arguments must be NVars).
• Derivatives (Multiple): variables to write derivatives. Order: der_coord0_var0, der_coord1_var0, ..., der_coord0_var1, der_coord1_var1, ...

They can be used independent from the dimensionality of the problem. For instance, readFromFileLinearWithDerivatives1D can be used in a 3D problem. In that way, a user could map a radial initial condition from a 3D problem, calculating the corresponding radius of a cell and passing it to the function.

• findCoordFromFile1D & findCoordFromFile2D & findCoordFromFile3D

Scope

Any section (Inside math tags). It also can be used in initial conditions or finalization conditions.

Infix

$fcff

Usage

The number of parameters are variable, depending on the number of coordinates and variables to get, findCoordFromFile(X)D(FileName, NCoords, NVars, OutputCoordIndex, CoordInputValues, ..., Var, VarIndex):

• FileName: name of the file to read from (without the .h5 extension).
• NCoords: number of coordinates in file.
• NVars: number of fields to read.
• OutputCoordIndex: index of the coordinate to return.
• CoordInputValues (Multiple): values for each coordinate to get position including an initial guess of the coordinate to obtain (number of arguments must be NCoords).
• Var: known value of the field.
• VarIndex: index of the given field.

Go to Simml reference.

Go to Simml context tags.

Go to Simml control tags.

Go to Simml data type tags.