A decoupled solution strategy for quasi-3D
finite element model of flow in multiaquifer systems
P. Teatini, G. Gambolati
Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
ABSTRACT
When groundwater flow takes place in aquifer-aquitard systems
characterized by highly hetereogeneous hydrogeological parameters with nonlinear behaviour,
quasi-3D models of flow
must be solved by a fully numerical approach.
The numerical implementation with finite difference or
finite element methods involves systems of large dimension whose solution
requires much CPU time and computer storage.
A new solution strategy of the resulting algebraic equations is
suggested to overcome the problem and is analyzed with linear porus media.
The global system is decoupled into a number of smaller
subsystems. The aquifers and the aquitards are solved separately,
and the final coupled solution is obtained with an iterative procedure. This
procedure is naturally suggested by the special sparsity pattern of the
coefficient matrix
and can be shown to be equivalent to a block SOR (successive over-relaxation)
strategy.
The SOR blocks correspond to the aquifer and aquitard equations.
The convergence property of the new scheme is analyzed, the optimum
over-relaxation factor is computed, and the asymptotic
convergence rate is theoretically analyzed in relation to the
hydrogeological parameters of the multiaquifer system.
