22.3 Viscosity

The viscosity unit physics/materialProperies/Viscosity implements a prescription for computing viscosity coefficients used by the Hydro PPM, the unsplit hydro and MHD solvers. In this release the unit provides support for two implementations. The Viscosity/ViscosityMain/Constant provides for either a constant dynamic viscosity or constant kinematic viscosity, where the choice between the two is made with the runtime parameter visc_whichCoefficientIsConst. The Viscosity/ViscosityMain/Spitzer unit implements an isotropic Spitzer type viscosity.

22.3.1 Constant Viscosity

To use viscosity in a FLASH4 simulation, the runtime parameter useViscosity must be set to .true. See Sec:Diffusion in the hydro module documentation for details on how the solver uses these modules. The viscosity sub-module implements a prescription for computing viscosity coefficients used by the hydro solver. To use viscosity in a FLASH simulation, the runtime parameter diffus_visc must be set to .true.. See Sec:Diffusion in the hydro module documentation for details on how the solver uses these modules.

22.3.2 Spitzer Viscosity

This module implements a coefficient of plasma ion viscosity according to the classical Spitzer(1962) prescription:

$$\mu_{ion} = \frac{0.406\cdot m_{ion}^{1/2} (kT_{ion})^{5/2}}{Z^4 e^4 \ln\Lambda}$$ (22.4)

$$= 2.21\cdot 10^{-15}\frac{A_{ion}^{1/2}T_{ion}^{5/2}}{Z^4 \log\Lambda}$$ (22.5)

and the usual units of a dynamic viscosity [gm cm$^{-1}$ sec$^{-1}$]. Here $m_{ion}$ is the ion mass, $T_{ion}$ is the ion temperature in Kelvin, $A$ is the dimensionless average atomic number, $Z$ is the dimensionless average ionization state, and $\log\Lambda$ is the ion-ion coulomb logarithm.
The kinematic viscosity is also computed as:

$$\nu_{ion} = \frac{\mu_{ion}}{\rho}$$ (22.6)

where $\rho$ is the fluid density, and the kinematic viscosity has units [cm$^2$ s$^{-1}$].