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  1. Jun 09, 2017
    • Andrew Heather's avatar
      TUT: Added min/max(p) function object · 132c0e71
      Andrew Heather authored
      132c0e71
    • Andrew Heather's avatar
      ENH: Added new Joule Heating fvOption and test case · 2af8d388
      Andrew Heather authored
          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
      2af8d388
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