User's guide of Proceessing Modflow 5.0

Processing Modflow 101
MODFLOW < Solvers
To calculate heads in each cell in the finite-difference grid, MODFLOW prepares one finite
difference equation for each cell, expressing the relationship between the head at a node and the
heads at each of the six adjacent nodes at the end of a time step. Because each equation may
involve up to seven unknown values of head, and because the set of unknown head values
changes from one equation to the next through the grid, the equations for the entire grid must be
solved simultaneously at each time step. The system of simultaneous finite difference linear
equations can be expressed in matrix notation as
A@x ' b
(3.30)
where A_ is a coefficient matrix assembled by MODFLOW using user-specified model data; b_
is a vector of defined flows, terms associated with head-dependent boundary conditions and
storage terms at each cell; x_ is a vector of hydraulic heads at each cell. One value of the hydraulic
head for each cell is computed at the end of each time step. At present PMWIN supports four
packages (solvers) for solving systems of simultaneous linear equations:
- the Direct Solution (DE45) package,
- the Preconditioned Conjugate-Gradient 2 (PCG2) package,
- the Strongly Implicit Procedure (SIP) package, and
- the Slice-Successive Overrelaxation(SSOR) package.
Input parameters of these solution methods are discussed below. See McDonald and Harbaugh
(1988), Hill (1990a) and Harbaugh (1995) for detailed mathematical background and numerical
implementation of these solvers. Various comparisons between the solution methods can be
found in Trescott (1977), Behie and Forsyth (1983), Scandrett (1989) and Hill (1990b). Hill
indicates that the greatest differences in solver efficiency on scalar computers occur for three-
dimensional, non-linear problems. For these types of problems, it may be well worth the time and
effort to try more than one solver. If your model does not have a large number of active cells, you
may try to use the direct solver (DE45). Otherwise, SIP generally is a good alternative to
consider.Note that the MODFLOW version “MODFLOW + Density package from KIWA” does
not support the Direction Solution package.
3.6.1 MODFLOW