Geoscience Reference
In-Depth Information
results of Haberli
et al.
5
,
8
to describe the photoionization and recombi-
nation reactions. The ionization frequency profiles of Cravens
et al.
7
take
into account the electron impact ionization. Schunk and Nagy
9
provide an
excellent review of the collision processes in planetary atmospheres. The
computation of the elastic collision effect between neutrals and ions and
between ions and electrons is based on their work. We used the theoretical
and experimental profiles of Itikawa
10
,
11
to incorporate the neutral-electron
collision effect. The electronic, vibrational, and rotation cooling of electrons
by water vapor is based on the study of Gan and Cravens.
12
2.2.
The adaptive mesh refinement technique
The size of the comet nucleus is of the order of 10 km, but the distance to
bow shock from the nucleus can be five orders of magnitude larger, and the
coma/tail extends downstream to a distance up to 10
8
km. To resolve the
finest of these scales while including the largest scale requires the use of a
mesh for the calculation that is adaptive and can adjust dynamically as the
structure in the solution evolves. To achieve this, the CASIM3D code uses
the PARAMESH tool kit of MacNeice
et al.
13
Figure 1 shows an example
of a 2-D adaptive mesh.
PARAMESH implements a subset of the Berger-Oliger type of block-
structured or patch-based adaptive mesh refinement.
14
,
15
In these schemes,
space is divided into a set of contiguous blocks. Each block is a Cartesian,
uniformly spaced sub-mesh. Each block can itself be refined into a set
of “child” blocks with half the grid spacing of their parent block. In
PARAMESH, space is recursively divided by bisecting the computational
volume in each coordinate direction. In a 3-D application, each block is a
structured sub-mesh with
n
x
×
n
z
cells, and each block has an iden-
tical number of cells. For CASIM3D,
n
x
=
n
y
=
n
z
= 4. PARAMESH
enforces the condition that jumps in resolution by more than a factor of 2
are not allowed. Each sub-mesh block is surrounded by guard cells so that
the mesh cells in the sub-mesh that are near to the sub-mesh boundary
have enough information about the solution in the neighboring sub-mesh
blocks. For CASIM3D, there are two layers of guard cells at each sub-mesh
boundary. PARAMESH fills these guard cells by copying data directly from
the neighboring blocks if the neighbor is at the same refinement level. In the
case of a refinement discontinuity at the block boundary the guard cells are
filled either by restriction if the neighboring sub-mesh is more refined or by
interpolation if it is less refined. PARAMESH allows the user to specify the
n
y
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