AN ADAPTIVE MESH REFINEMENT ALGORITHM FOR THE RADIATIVE TRANSPORT-EQUATION

The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits local grid refinement to minim ize spatial discretization error of the RTE. An error estimator is app lied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then sol ved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The follo wing aspects of the algorithm are discussed: error estimation, grid ge neration, communication between refined levels, and solution sequencin g. This initial formulation employs the step scheme and is valid for a bsorbing and isotropically scattering media in two-dimensional enclosu res. The utility of the algorithm is tested by comparing the convergen ce characteristics and accuracy to those of the standard single-grid a lgorithm. For two simple benchmark problems, the AMR algorithm maintai ns the convergence characteristics of the standard single-grid algorit hm, but it does not provide any efficiency gains due to a lack of disp arate spatial scales. In a third, mon localized problem, however, the AMR algorithm demonstrates significant memory and CPU time reductions. (C) 1998 Academic Press.