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spatial and temporal discretization of the governing advection-dispersion equation, depends upon
the value of the temporal weighing factor, ε. The explicit (ε=0) and fully implicit (ε=1) schemes
require that the global matrix [G] and the vector {g} be evaluated at only one time level (the
previous or current time level). The other two schemes require evaluation at both time levels. Also,
the Crank-Nicholson and implicit schemes lead to an asymmetric banded matrix [G]. By contrast,
the explicit scheme (ε=0) leads to a diagonal matrix [G] which is much easier to solve (but generally
requires much smaller time steps).
The Crank-Nicholson centered scheme is recommended in view of solution precision. The fully
implicit scheme also leads to numerical dispersion, but is better in avoiding numerical instabilities.
The explicit scheme is most prone to numerical instabilities with undesired oscillations (and is
currently disabled).
b) Space Weighting Scheme
HYDRUS provides three options for the Space Weighting Scheme, i.e., the regular Galerkin
Finite Elements formulation, the Upstream Weighting Finite Elements formulation, and the
Galerkin Finite Elements formulation with Artificial Dispersion.
While the Galerkin Finite Elements formulation is recommended in view of solution precision,
Upstream Weighting is provided as an option in HYDRUS to minimize some of the problems with
numerical oscillations when relatively steep concentration fronts are being simulated. For this
purpose the second (flux) term of advective-dispersive equation is not weighted by regular linear
basis functions, but instead using nonlinear functions [Yeh and Tripathi, 1990]. The weighing
functions ensure that relatively more weight is placed on flow velocities of nodes located at the
upstream side of an element.
Additional Artificial Dispersion may be added also to stabilize the numerical solution and to
limit or avoid undesired oscillations in the Galerkin finite element results. Artificial dispersion is
added such that a Stability Criterion involving Pe.Cr (the product of the Peclet number and the
Curant number) [Perrochet and Berod, 1993] is satisfied. The recommended value for Pe.Cr is
2.0.
c) Solute Information
Number of Solutes
Number of solutes to be simulated simultaneously or involved in a
decay chain reaction.
Pulse Duration
Time duration of the concentration pulse. Concentrations (flux or
resident) along all boundaries, for which no time-variable
boundary conditions are specified, are then set equal to zero for
times larger than the "Pulse Duration". When the Fumigant option
is active, this variable is used instead to define Time of Tarp
Removal.
Mass Units
Units to be printed to the output files or displayed in various
graphs. Mass units have no effect on the calculations.
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