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Commit 2af8d388 authored by Andrew Heather's avatar Andrew Heather
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ENH: Added new Joule Heating fvOption and test case

    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
parent caf9a087
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