PDEModelica1¶
PDEModelica1 is nonstandardised experimental Modelica language extension for 1dimensional partial differential extensions (PDE).
It is enabled using compiler flag grammar=PDEModelica
. Compiler flags may be set e.g. in OMEdit (Tools>Options>Simulation>OMC Flags) or in the OpenModelica script using command. Note that PDEModelica does now work yet with the current frontend so you need to set d=newInst
in Tools>Options>Simulation>OMC Flags or check "Enable old frontend for code generation".
PDEModelica1 language elements¶
Let us introduce new PDEModelica1 language elements by an advection equation example model:
model Advection "advection equation"
parameter Real pi = Modelica.Constants.pi;
parameter DomainLineSegment1D omega(L = 1, N = 100) "domain";
field Real u(domain = omega) "field";
initial equation
u = sin(2*pi*omega.x) "IC";
equation
der(u) + pder(u,x) = 0 indomain omega "PDE";
u = 0 indomain omega.left "BC";
u = extrapolateField(u) indomain omega.right "extrapolation";
end Advection;
Error
[<interactive>:4:144:14:writable] Error: Missing token: SEMICOLON
The domain omega
represents the geometrical domain where the PDE holds. The domain is
defined using the builtin record DomainLineSegment1D
. This record contains among
others L
 the length of the domain, N
 the number of grid points, x

the coordinate variable and the regions left
, right
and interior
, representing
the left and right boundaries and the interior of the domain.
The field variable u
is defined using a new keyword field
. The domain
is a mandatory attribute to specify the domain of the field.
The indomain
operator specifies where the equation containing the field variable holds. It
is utilised in the initial conditions (IC) of the fields, in the PDE and in the boundary
conditions (BC). The syntax is
anEquation indomain aDomain.aRegion;
If the region is omitted, interior
is the default (e.g. the PDE in the example above).
The IC of the field variable u is written using an expression containing the coordinate
variable omega.x
.
The PDE contains a partial space derivative written using the pder
operator. Also
the second derivative is allowed (not in this example), the syntax is e.g. pder(u,x,x)
.
It is not necessary to specify the domain of coordinate in pder (to write e.g. pder(u,omega.x)
, even though x
is a member of omega
.
Limitations¶
BCs may be written only in terms of variables that are spatially differentiated currently.
All fields that are spatially differentiated must have either BC or extrapolation at each
boundary. This extrapolation should be done automatically by the compiler, but this has
not been implemented yet. The current workaround is the usage of the extrapolateField()
operator directly in the model.
Ifequations are not spported yet, ifexpressions must be used instead.
Viewing results¶
During translation field variables are replaced with arrays. These arrays may be plotted using arrayplot or even better using Array Parametric Plot (to plot xcoordinate versus a field).