PICARD AND NEWTON LINEARIZATION FOR THE COUPLED MODEL OF SALTWATER INTRUSION IN AQUIFERS

Difficulties in the numerical solution of the partial differential equ ations governing seawater intrusion in aquifers arise from the couplin g between the flow and transport equations and from the nonlinear aspe cts of this coupling. Several linearization approaches are discussed f or the solution of the nonlinear system which results from a finite el ement discretization of the coupled equations. It is first shown that the most commonly used solution method can be viewed as a Picard linea rization applied to the transport equation, with the coupling resolved by iteration over the two governing equations. The full Newton scheme for solving the coupled problem produces a Jacobian of size 2N x 2N, where N is the number of nodes in the discretization of both the flow and transport equations. To reduce the size and complexity of the full Newton scheme, a partial Newton method is proposed, which, like the P icard approach, produces matrix systems of size N x N. This scheme app lies Newton linearization to the transport equation, and conventional iteration to resolve the coupling. Results from two- and three-dimensi onal test simulations show that the partial Newton scheme gives improv ed convergence and robustness compared to Picard linearization, especi ally for highly advective problems or large density ratios. Both appro aches involve the solution of a symmetric (flow) and a nonsymmetric (t ransport) system of equations, and it is shown that the per iteration CPU cost for the partial Newton method is not significantly greater th an that of the Picard scheme.