Authors:  C. T. Kelley, C. T. Miller, and M. D. Tocci

Speaker: M. D. Tocci

Method of Lines Solution of Richards' Equation

We consider the method of lines solution of Richards' equation, which 
models flow through porous media, as an example of a situation in which 
the method can give incorrect results because of premature termination of the
nonlinear corrector iteration. This premature termination arises when
the solution has a sharp moving front and the Jacobian is ill-conditioned.
While this problem can be solved by tightening the tolerances provided
to the ODE or DAE solver used for the temporal integration, it is more
efficient to modify the termination criteria of the nonlinear solver
and/or recompute the Jacobian more frequently. In this paper we continue
previous work on this topic by analyzing the modifications in more detail
and giving a strategy on how the modifications can
be turned on and off in response to changes in the character of the solution.