add documentation of conducitivities and opacities

sphinx_docs/source/refs.bib

@@ -625,3 +625,18 @@ @misc{autodiff
     howpublished = {\texttt{https://autodiff.github.io}},
     year = {2018}
 }
+
+@ARTICLE{timmes:2000,
+       author = {{Timmes}, F.~X.},
+        title = "{Physical Properties of Laminar Helium Deflagrations}",
+      journal = {\apj},
+     keywords = {HYDRODYNAMICS, METHODS: NUMERICAL, NUCLEAR REACTIONS, NUCLEOSYNTHESIS, ABUNDANCES, STARS: INTERIORS, Hydrodynamics, Methods: Numerical, nuclear reactions, nucleosynthesis; abundances, Stars: Interiors},
+         year = 2000,
+        month = jan,
+       volume = {528},
+       number = {2},
+        pages = {913-945},
+          doi = {10.1086/308203},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/2000ApJ...528..913T},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}

sphinx_docs/source/transport.rst

@@ -5,15 +5,130 @@ Transport Coefficients
 Thermal Conductivity
 ====================
 
-Thermal conductivities are provided by the conductivity/
-directory. At the moment, there is a single version,
-stellar [1]_ that is useful
-for stellar interiors.
-
-**Important: it is assumed that the state is thermodynamically consistent
-before calling the conductivity routine.** It may be necessary to do an EOS
-call first, to enforce the consistency.
-
-.. [1]
-   this code comes from Frank Timmes’ website,
-   https://cococubed.com/code_pages/kap.shtml
+The thermal conductivities, $k_\mathrm{th}$, are provided to allow for
+modeling of thermal diffusion, for instance in an energy equation:
+
+.. math::
+
+   \frac{\partial (\rho e)}{\partial t} = \nabla \cdot k_\mathrm{th} \nabla T
+
+Thermal conductivities are provided by the ``conductivity/``
+directory.  The main interface has the form:
+
+.. code:: c++
+
+   template <typename T>
+   AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
+   void conductivity (T& state)
+
+where currently, the input type needs to be the full EOS type, ``eos_t``.  The conductivity
+is then available as ``eos_t eos_state.conductivity``.
+
+.. important::
+
+   It is assumed that the state is thermodynamically consistent
+   before calling the conductivity routine.
+   It may be necessary to do an EOS
+   call first, to enforce the consistency.
+
+There are several implementations of the conductivity currently:
+
+* ``constant`` :
+
+  This simply sets the conductivity to a constant value set via
+  ``conductivity.const_conductivity``.
+
+* ``constant_opacity`` :
+
+  This is intended for creating a conductivity from an opacity, for
+  instance, electron scattering.  The opacity is taken as constant
+  and set via ``conductivity.const_opacity``, and then the conductivity
+  is set as:
+
+  .. math::
+
+     k_\mathrm{th} = \frac{16 \sigma_\mathrm{SB} T^3}{3 \kappa \rho}
+
+  where $\sigma_\mathrm{SB}$ is the Stefan-Boltzmann constant.
+
+* ``powerlaw`` :
+
+  This models a temperature-dependent conductivity of the form:
+
+  .. math::
+
+     k_\mathrm{th} = k_0 T^\nu
+
+  where $k_0$ is set via ``conductivity.cond_coeff`` and $\nu$ is set via
+  ``conductivity.cond_exponent``.
+
+* ``stellar`` :
+
+  This is a general stellar conductivity based on :cite:`timmes:2000`.
+  It combines radiative opacities and thermal conductivities into a
+  single expression.  This conductivity is suitable for modeling
+  laminar flames.
+
+.. index:: CONDUCTIVITY_DIR
+
+These can be set via the ``CONDUCTIVITY_DIR`` make variable.
+
+
+Radiation Opacities
+===================
+
+For radiation transport, we provide simple opacity routines that return
+the Planck and Rosseland mean opacities.
+
+The interface for these opacities is:
+
+.. code:: c++
+
+   AMREX_GPU_HOST_DEVICE AMREX_INLINE
+   void actual_opacity (Real& kp, Real& kr, Real rho, Real temp, Real rhoYe, Real nu,
+                        bool get_Planck_mean, bool get_Rosseland_mean)
+
+where the boolean ``get_Planck_mean`` and ``get_Rosseland_mean`` specify where those
+opacity terms are filled upon return.
+
+There are 2 interfaces, which are selected via the make variable ``Opacity_dir``.
+
+* ``breakout`` :
+
+  This returns a simple electron scattering opacity with a crude approximation
+  connecting the Planck and Rosseland means.
+
+* ``rad_power_law`` :
+
+  This constructs a power-law opacity.  For the Planck mean, it is:
+
+  .. math::
+
+     \kappa_p = \kappa_{p,0} \rho^{m_p} T^{-{n_p}} \nu^{p_p}
+
+  where $\kappa_{p,0}$ is set via ``opacity.const_kappa_p``, $m_p$ is set via ``opacity.kappa_p_exp_m``,
+  $n_p$ is set via ``opacity.kappa_p_exp_n``, and $p_p$ is set via ``opacity.kappa_p_exp_p``.
+
+  The Rosseland mean has a scattering component, $\kappa_s$, which is computed as:
+
+  .. math::
+
+     \kappa_s = \kappa_{s,0} \rho^{m_s} T^{-{n_s}} \nu^{p_s}
+
+  where $\kappa_{s,0}$ is set via ``opacity.const_scatter``, $m_s$ is set via ``opacity.scatter_exp_m``,
+  $n_s$ is set via ``opacity.scatter_n``, and $p_s$ is set via ``opacity.scatter_p``.  The Rosseland
+  mean is then computed as:
+
+  .. math::
+
+     \kappa'_r = \kappa_{r,0} \rho^{m_r} T^{-{n_r}} \nu^{p_r}
+
+  where $\kappa_{r,0}$ is set via ``opacity.const_kappa_r``, $m_r$ is set via ``opacity.kappa_r_exp_m``,
+  $n_r$ is set via ``opacity.kappa_r_exp_n``, and $p_r$ is set via ``opacity.kappa_r_exp_p``, and then
+  combined with scattering as:
+
+  .. math::
+
+     \kappa_r = \max \{ \kappa'_r + \kappa_s, \kappa_\mathrm{floor} \}
+
+  where $\kappa_\mathrm{floor}$ is set via ``opacity.kappa_floor``,