User's guide of Proceessing Modflow 5.0

Processing Modflow 177
all velocity terms in equations 4.3a - 4.3f by -1.
For transient flow fields, in addition to the condition for stready-state flow fields, t and t
1 2
must lie within the same time step. In PMPATH, each particle may be associated with a set of
attributes, i.e., the retardation factor, the starting, forward and backward travel times and
positions. If a particle is travelling across the end (forward tracking) or the beginning (backward
tracking) of a time step of a flow simulation, PMPATH sets t to the end or beginning time of this
2
time step and forces the particle to wait until the flow field of the next time step (forward
tracking) or the previous time step (backward tracking) is read. If the end or beginning time of
a transient flow simulation is reached, the most recent flow field can be treated as steady-state
and the movement of particles can go on.
Consideration of the display of the calculated pathlines
Because of the capability of calculating particle’s exit point from a cell directly, pathlines
displayed by PMPATH may sometimes intersect each other. Consider the case shown in Fig. 4.4,
two particles within a two-dimensional cell start at the same time. The dashed curves represent
the actual paths of these two particles. The solid lines are the pathlines displayed by PMPATH.
The pathlines intersect each other, although the particles’ exit points are exactly equal to that of
the actual paths. This effect can be prevented by using a smaller particle tracking step length such
that intermediate particle positions between starting point and exit point can be calculated. See
Particle Tracking (Time) Properties dialog box (sec. 4.3) for how to change the particle
tracking step length.
Consideration of the spatial discretization and water table layers
The method described above is based on the assumption that the model domain was discretized
into an orthogonal finite-difference mesh, i.e., all model cells in the same layer have the same
thickness. In practice, variable layer thickness is often preferred for approaching varying
thicknesses of stratigraphic geohydrologic units. In order to calculate approximate groundwater
paths for this kind of discretization, PMPATH (as well as MODPATH) uses a vertical local
coordinate instead of the real-world z-coordinate. The vertical local coordinate is defined for
each cell as
z L ' (z & z 1 ) / (z 2 & z 1 )
(4.7)
where z and z are the elevations of the bottom and top of the cell, respectively. According to
1 2
this equation, the vertical local coordinate z is equal to 0 at the bottom of the cell and z is equal
L L
4.1 The Semi-analytical Particle Tracking Method