Evolves an electrical potential equation
\f[
\grad \left( \sigma \grad V \right)
\f]
where \f$ V \f$ is electrical potential and \f$\sigma\f$ is the
electrical current
To provide a Joule heating contribution according to:
Differential form of Joule heating - power per unit volume:
\f[
\frac{d(P)}{d(V)} = J \cdot E
\f]
where \f$ J \f$ is the current density and \f$ E \f$ the electric
field.
If no magnetic field is present:
\f[
J = \sigma E
\f]
The electric field given by
\f[
E = \grad V
\f]
Therefore:
\f[
\frac{d(P)}{d(V)} = J \cdot E
= (sigma E) \cdot E
= (sigma \grad V) \cdot \grad V
\f]
Usage
Isotropic (scalar) electrical conductivity
\verbatim
jouleHeatingSourceCoeffs
{
anisotropicElectricalConductivity no;
// Optionally specify the conductivity as a function of
// temperature
// Note: if not supplied, this will be read from the time
// directory
sigma table
(
(273 1e5)
(1000 1e5)
);
}
\endverbatim
Anisotropic (vectorial) electrical conductivity
jouleHeatingSourceCoeffs
{
anisotropicElectricalConductivity yes;
coordinateSystem
{
type cartesian;
origin (0 0 0);
coordinateRotation
{
type axesRotation;
e1 (1 0 0);
e3 (0 0 1);
}
}
// Optionally specify sigma as a function of temperature
//sigma (31900 63800 127600);
//
//sigma table
//(
// (0 (0 0 0))
// (1000 (127600 127600 127600))
//);
}
Where:
\table
Property | Description | Required | Default
value
T | Name of temperature field | no | T
sigma | Electrical conductivity as a function of
temperature |no|
anisotropicElectricalConductivity | Anisotropic flag | yes |
\endtable
The electrical conductivity can be specified using either:
- If the \c sigma entry is present the electrical conductivity is
specified
as a function of temperature using a Function1 type
- If not present the sigma field will be read from file
- If the anisotropicElectricalConductivity flag is set to 'true',
sigma
should be specified as a vector quantity
- the heuristic for matching unresolved intersections is a relatively
simple matching scheme that seems to be more robust than attempting to walk
the geometry or the cuts.
- avoid false positives for self intersection
- ensure that each have found() and which() methods
- add faceTraits for handling compile-time differences between
'normal' and tri-faces
- provide line::unitVec method (complimentary to edge::unitVec)
- provide key_iterator/const_key_iterator for all hashes,
reuse directly for HashSet as iterator/const_iterator, respectively.
- additional keys() method for HashTable that returns a wrapped to
a pair of begin/end const_iterators with additional size/empty
information that allows these to be used directly by anything else
expecting things with begin/end/size. Unfortunately does not yet
work with std::distance().
Example,
for (auto& k : labelHashTable.keys())
{
...
}
- add increment/decrement, repositioning. Simplify const_iterator.
- this makes is much easier to use labelRange for constructing ranges of
sub-lists. For symmetry with setSize() it has a setStart() instead of
simply assigning to start() directly. This would also provide the
future possibility to imbue the labelRange with a particular policy
(eg, no negative starts, max size etc) and ensure that they are
enforced.
A simple use case:
// initialize each to zero...
List<labelRange> subListRanges = ...;
// scan and categorize
if (condition)
subListRanges[categoryI]++; // increment size for that category
// finally, set the starting points
start = 0;
for (labelRange& range : subListRanges)
{
range.setStart(start);
start += range.size();
}
