Prescribed dilation#
Subsection: Prescribed dilation#
Parameter: List of model names
Default value:
Pattern: [MultipleSelection function ]
Documentation: A comma separated list of dilation models that will be used to calculate the source term in the continuity equation.
The following dilation models are available:
‘function’: Prescribed dilation is given in terms of an explicit formula that is elaborated in the parameters in section “Prescribed dilation|Function”. The format of these functions follows the syntax understood by the muparser library, see How to write Function expressions in parameter files.
Physical units: \(\mathrm{s}^{-1}\).
Subsection: Prescribed dilation / Function#
Parameter: Coordinate system
Default value: cartesian
Pattern: [Selection cartesian|spherical|depth ]
Documentation: A selection that determines the assumed coordinate system for the function variables. Allowed values are ‘cartesian’, ‘spherical’, and ‘depth’. ‘spherical’ coordinates are interpreted as r,phi or r,phi,theta in 2d/3d respectively with theta being the polar angle. ‘depth’ will create a function, in which only the first parameter is non-zero, which is interpreted to be the depth of the point.
Parameter: Function constants
Default value:
Pattern: [Anything]
Documentation: Sometimes it is convenient to use symbolic constants in the expression that describes the function, rather than having to use its numeric value everywhere the constant appears. These values can be defined using this parameter, in the form ‘var1=value1, var2=value2, …’.
A typical example would be to set this runtime parameter to ‘pi=3.1415926536’ and then use ‘pi’ in the expression of the actual formula. (That said, for convenience this class actually defines both ‘pi’ and ‘Pi’ by default, but you get the idea.)
Parameter: Function expression
Default value: 0
Pattern: [Anything]
Documentation: The formula that denotes the function you want to evaluate for particular values of the independent variables. This expression may contain any of the usual operations such as addition or multiplication, as well as all of the common functions such as ‘sin’ or ‘cos’. In addition, it may contain expressions like ‘if(x>0, 1, -1)’ where the expression evaluates to the second argument if the first argument is true, and to the third argument otherwise. For a full overview of possible expressions accepted see the documentation of the muparser library at http://muparser.beltoforion.de/.
If the function you are describing represents a vector-valued function with multiple components, then separate the expressions for individual components by a semicolon.
Parameter: Variable names
Default value: x,y,t
Pattern: [Anything]
Documentation: The names of the variables as they will be used in the function, separated by commas. By default, the names of variables at which the function will be evaluated are ‘x’ (in 1d), ‘x,y’ (in 2d) or ‘x,y,z’ (in 3d) for spatial coordinates and ‘t’ for time. You can then use these variable names in your function expression and they will be replaced by the values of these variables at which the function is currently evaluated. However, you can also choose a different set of names for the independent variables at which to evaluate your function expression. For example, if you work in spherical coordinates, you may wish to set this input parameter to ‘r,phi,theta,t’ and then use these variable names in your function expression.