Introduction

  test_advect is a simple test of the advection scheme only.  In short
  we:

    -- set up a unit cube (or equivalent in lower dimensions) with 
       periodic boundaries

    -- initialize a constant velocity field in one of the coordinate
       directions

    -- initialize the density field to a gaussian

    -- estimate a timestep

    -- use density_advance to update the density field only.



Computing the Norm of the Error

  test_advect produces an output file at the start (dens_orig) and one
  at the very end (dens_??_final), where ?? is one of
  {xm,xp,ym,yp,zm,zp} indicating the coordinate direction of the
  advection and whether it was `+' or `-'.

  The fcompare tool (in fParallel/data_processing/) computes the L2
  norm of the error and relative error of each variable in a plotfile
  on a level-by-level basis.  It requires that the grids be identical.

  To get the L2 error after advecting in the +X direction, we would
  do:

    fcompare.Linux.Intel.exe --infile1 dens_orig --infile2 dens_xp_final

  which gives:

    level =            1
     density               5.621649219909652E-002   97.5143285214983     

  Here, the only variable in the file, "density" is listed with two
  numbers following, the L2 error and L2 relative-error.  In this
  case, the relative error is likely set where the densities are tiny,
  and is not too meaningful.

 