Diffusion Processes

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 $\boldsymbol{Q}$ is defined by

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

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

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