This document describes a 1D hydrodynamic solver including time evolution of atoms/ions. It is written in IDL. An elementary but modern, method is used 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 Astrophysical Journal, 402, 741-755). Heating is added explicitly, radiation losses are included via a lookup table, conduction is computed explicitly. In short:
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 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 (when param.tvorder=2, otherwise just the first order predictor step is used). The vectors u are
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 algorithm is not efficient nor elegant, but results 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 chromopshere at the other footpoint. It is interesting that an equilibrium has not been found- perhaps this is related to Athay's (2000) proposal that there is an ionization instability at the coronal base.
main
states
initial
states
atmosrd
doublit
specno
seqtri
gravity
cpcv
uplot
states
tvdlf
delubar
minmod
call_function(param.driver)
changes
source
flux
csound
impstep
bound
boundaries
Each function/procedure is briefly documented as to its function in the procedure's header.
Using the SSWIDL environment, simply unpack the tarball. Move to the sub-directory
examplewhich contains two files needed to set some parameters. Edit the file
inpt !! EDIT THISto point to the datadir directory on your system), start sswidl, and type
IDL> .run main
A window will pop up which lists the input parameters (it is an "xstruct" window IDL> xstruct,param,/edit): you can edit the values there, click commit and the program should run.
Here is a list of parameters:IDL> help,param ** Structure <31f1208>, 31 tags, length=320, data length=306, refs=1: GAMMA DOUBLE 1.6666667 BCONST DOUBLE 1.3806200e-16 ECHARGE DOUBLE 1.6021890e-12 MU DOUBLE 1.3625000 UMASS DOUBLE 1.6600000e-24 SIGMA DOUBLE 5.6695600e-05 KAPPA0 DOUBLE -1.0000000e-06 ALPHA DOUBLE 2.5000000 GRAV DOUBLE -27542.291 HEATP DOUBLE 2.0000000e-12 HEATN DOUBLE 2.0000000e-14 DRIVER STRING 'burst3e' ELEMENTS STRING Array[5] SPECMIN INT Array[5] SPECMAX INT 8 DATADIR STRING '/Users/judge/Projects/1dhd/datadir/' NX INT 1025 XMIN DOUBLE 80000000. XMAX DOUBLE 2.0839139e+09 LIMITER STRING 'superbee' TVORDER INT 1 RESTART INT 2 SOURCE_MULT DOUBLE 1.0000000 SLOWDOWN DOUBLE 5.0000000 IMPLICIT DOUBLE 0.0000000 COURANT_N DOUBLE 0.80000000 TSMALL DOUBLE 1.0000000e-05 TMAX INT 30 OSPLIT INT 1 DEBUG INT 0 IELEMENTS INT Array[5]
See the files
inpt
for a description of these parameters. This file sets default parameter values, which can be edited using the window which pops up after executing the IDL>.run main command.
Here is the popup window, only scalar values can be edited here.
xstruct window, the scalar values can be edited and pressing "commit" will run the program, integrating up the state variables in time.
During run time, two windows pop up. Examples are given here:
Snapshot of the evolution of thermodynamic parameters.
Snapshot of instantaneous changes in time, of the state variables as a function of position along the loop, x. In this case the state variables are rho, rho.v, total energy, hydrogen and proton densities, and the densities of neutral, ionized and doubly ionized helium, and of various ionization stages of carbon , oxygen, and silicon.
The "changes" image plot can be used to see what variables are changing the most and therefore, what variables determine the time step sizes used. this can be handy to see why the code runs slowly under certain conditions (steep gradients in temperature tend to do this).
Just to look at a run afterwards simply do
IDL> umovie
This procedure loops over the saved files u*sav and plots the evolution of the gas dynamic variables.
To examine the data carefully you can select a timestep, the data are currently saved once every second, by doing
IDL> restore,/verb,'u100.sav' ; restore the 100 second calculation IDL> pp=pnt(u) ; variable pp contains the presure, number density, temperature IDL> plot,x, pp(0,*) ; plot pressure against distance along the loop IDL> plot,x, u(3,*) ; plot neutral hydrogen number density against distance along the loop IDL> desc=states() ; get the names of the states which are solved for IDL> print,desc ; look at the state names IDL> plot,x,u(k,*) ; plot state k against x.
Note that the conserved variables are rho, rhoV, total energy, these are in u(0,*), u(1,*), u(2,*), so that the function pnt(u) returns pressure, number density and temperature from these variables.
To look the emission lines after the fact, use at a run afterwards simply do
IDL> postproc, lines, emissivity IDL> k=where(lines.lambda gt 1547. and lines.lambda lt 1549.) ; select line IDL> plot_image,reform(emissivity(k(0),*,*)) ; display emissivity as fn. of x and time
linesis an IDL structure, and emissivity is the computed emissivity for each line:
emissivity(line_index, x, time)Use
IDL> help,/structure,lines
to see what the structure variables are.