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Diffusion Processes

Last edited by Patrick Mullen

Diffusion processes implemented in AthenaK include:

  • Hydrodynamic diffusion: fluid viscosity and thermal conduction
  • Field diffusion: Ohmic diffusion

Input File

Diffusive physics such as viscosity and/or thermal conduction can be constructed in <hydro> or <mhd>. Ohmic diffusion is constructed in <mhd> block. They are enrolled in the corresponding <block> in the input file:

<hydro>
viscosity   = 1.0e-3   # coefficient of isotropic shear viscosity
conductivity = 1.0e-3  # coefficient of isotropic thermal conduction

or

<mhd>
viscosity   = 1.0e-3     # coefficient of isotropic shear viscosity
conductivity = 1.0e-3    # coefficient of isotropic thermal conduction
ohmic_resistivity = 0.01 # coefficient of Ohmic resistivity

Thermal conduction

The heat flux

Q\boldsymbol{Q}
is defined by

Q=−K∇T, \boldsymbol{Q}=-\mathcal{K}\nabla T,

where the coefficient

K\mathcal{K}
is the conductivity. The current implementation uses a dimensionless system of units (see Units) in that the factor
(mˉ/kB)(\bar{m}/k_{\rm B})
is not included in calculating the temperature. Instead,
T=P/ρT=P/\rho
is adopted. Users must use dimensionless conductivity as the input parameter.

Note that the coefficient

K\mathcal{K}
corresponds to conductivity, not a diffusivity. This is different from the coefficient used in Athena++.

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