Here are contained some calculations using a crude, but modern, method to solve for the equations of conservation of mass, momentum, energy and non-equilibrium number densities of species of H, He, C, ... within the solar atmosphere, in 1D. The equations solved are essentially those of Hansteen 1993. Heating is added explicitly, radiation losses are included via a lookup table, conduction is computed explicitly.
The presence of heat conduction makes the equations highly non-linear- the time steps are adjusted so that only small steps in time are taken to ensure the intrinsic second order accuracy of the method.
The code is written in IDL. It is not quite ready for others to use but is getting close.
The method used is an explicit time integration of the governing equations on a fixed grid, written in conservative form, using the Total Variation Diminishing Scheme concept. Here a Lax-Friedrich scheme (TVDLF) is adopted (predictor-corrector) to update solution vectors u as a function of time,
u(state, position)
Here the vector u specifies a physical variable [cgs units]:
u(0,*)= density
u(1,*)= density*velocity
u(2,*)= total energy density (internal plus thermal and kinetic)
u(3,*)= neutral hydrogen population density
u(4,*)= proton population density
If present, the remaining components (u(5....n,*)) contain number densities of He, He+, He++, C, C+, C++ ....
The solutions are not efficient nor elegant, but they appear to be correct. Results are stored in files
u0.sav (state at time t=0)
u1.sav (state at time t=1 sec)
...
uN.sav (state at time t=N, N integer sec)
Here is a gif movie of the evolution of vector u starting from a VAL-like atmosphere, but which is heated at constant rates per proton which is 50x that per hydrogen atom. The x-axes are "distance along a complete loop", from chromosphere into the corona and back down into the chromosphere at the other footpoint. After 2 seconds the gas is forced by an upward acceleration and additional heating in the upper chromosphere.
