AN OPTIMAL-CONTROL LEAST-SQUARES METHOD FOR THE SOLUTION OF ADVECTION-DISPERSION PROBLEMS

This paper discusses the numerical solution of advection dispersion eq uations using an Optimal control, H-1, least-squares formulation, asso ciated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeaux et al., for the solution of nonlinear fluid flow problems. At each ti me step, the discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization one, whose objective function allows the capture of the a dvective behavior of the equation for high values of the P(e) number. A general presentation is made of the optimization algorithm. Validati on runs, for a one-dimensional example, show fairly accurate results f or a wide range of Peclet and Courant numbers. Comparisons with severa l numerical schemes are also presented.