THE CONVERGENCE OF NUMERICAL TRANSFER SCHEMES IN DIFFUSIVE REGIMES I: DISCRETE-ORDINATE METHOD FRANC

In highly diiusive regimes, the transfer equation with anisotropic boundary conditions has an asymptotic behavior as the mean free path tends to zero that is governed by a diiusion equation and boundary conditions obtained through a matched asymptotic boundary layer analysis. A numerical scheme for solving this problem has a ?1 contribution to the truncation error that generally gives rise to a nonuniform consistency with the transfer equation for small , thus degrading its performance in diiusive regimes. In this paper we show that whenever the discrete-ordinate method has the correct diiusion limit, both in the interior and at the boundaries, its solutions converge to the solution of the transport equation uniformly in. Our proof of the convergence is based on an asymptotic diiusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete-ordinate method.