PDEModelica documentation.

UsersGuide/source/index.rst

@@ -27,6 +27,7 @@ Generated on |date| at |time|
   omsimulator
   optimization
   parametersensitivity
+  pdemodelica
   mdt
   mdtdebugger
   profiler

UsersGuide/source/omedit.rst

@@ -504,6 +504,8 @@ windows by clicking on the New Plot Parametric toolbar button (|parametric-plot-
   :alt: OMEdit New Parametric Plot Window Icon
   :height: 14pt
 
+.. _array-plot :
+
 Array Plot
 ^^^^^^^^^^
 
@@ -518,6 +520,8 @@ A new Array Plot window is opened using the New Array Plot Window toolbar button
   :alt: OMEdit New Array Plot Window Icon
   :height: 14pt
 
+.. _array-parametric-plot :
+
 Array Parametric Plot
 ^^^^^^^^^^^^^^^^^^^^^
 

UsersGuide/source/pdemodelica.rst

@@ -0,0 +1,75 @@
+PDEModelica1
+============
+
+PDEModelica1 is nonstandardised experimental Modelica language extension for 1-dimensional 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
+
+.. omc-mos ::
+  setCommandLineOptions("--grammar=PDEModelica")
+
+
+PDEModelica1 language elements
+------------------------------
+
+Let us introduce new PDEModelica1 language elements by an advection equation example model:
+
+
+.. omc-loadstring ::
+
+  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;
+
+The domain ``omega`` represents the geometrical domain where the PDE holds. The domain is
+defined using the built-in 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.
+
+If-equations are not spported yet, if-expressions must be used instead.
+
+Viewing results
+---------------
+
+During translation field variables are replaced with arrays. These arrays may be plotted using :ref:`array-plot` or even better using :ref:`array-parametric-plot` (to plot x-coordinate versus a field).
+
+
+
+.. omc-reset ::