Parallel block iterative method for multiaquifer flow models
G. Pini, P. Teatini,
Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
ABSTRACT
Flow in multiaquifer porous system can be simulated by the so
called ''quasi three-dimensional'' models. When heterogeneous and/or
aquitards with non-linear hydrogeologic behavior are considered, a fully
numerical approach is required for the model solution. If the
finite element method is used to integrate the partial differential flow
equations, the final solution of large systems is required.
In the present paper an original iterative solution strategy is
developed.
The global system is decoupled into a number of smaller subsystems
consistent with the geologic structure (aquitards and aquifers) of the
multiaquifer system. The
aquifer and the aquitard equations are solved separately with the
modified conjugate gradient and the Thomas algorithms, respectively,
while the final coupled solution is obtained with an iterative
procedure equivalent to a Block Jacobi scheme. The procedure can be
efficiently implemented on a parallel super-computer distributing the computational load
so that two successive blocks (related to an aquifer and the
underlying aquitard) are solved on the same processor.
The procedure is analyzed with linear porous media, where the convergence
is theoretically ensured. The results obtained with a
realistic linear multiaquifer system, employing a massively parallel
computer like the CRAY T3D,
have pointed out the high degree of parallelization of the algorithm.
Comparison with the parallel implementation of the Block SOR and
Block Gauss-Seidel schemes shows that parallel Block Jacobi
performs significantly better with a reduction
of the elapsed times which depends on the rate of leakage between
neighbouring aquifers.
