A LEAST-SQUARES PROCEDURE FOR THE SOLUTION OF TRANSPORT PROBLEMS

In this paper a least‐squares formulation associated with a conjugate gradient algorithm is proposed for the solution of transport problems. In this procedure the advection–diffusion equation is first discretized in time using an implicit scheme. At each time step the resulting partial differential equation is replaced by an optimal control problem. This minimization problem involves the minimization of a functional defined via a state equation. This functional is chosen in order to force the numerical solution of the advection–diffusion equation to be equal to the hyperbolic advective part of this equation. The effectiveness of the method is shown through a one‐dimensional example involving advective and diffusive transport. No oscillation and high accuracy have been obtained for the entire range of Peclet numbers with a Courant number well in excess of unity. Copyright © 1990 John Wiley & Sons, Ltd