Specifically, we present an iteration algorithm based on the nonlinear averaged flux (AF) method [9, 10], also
Recently, several nonlinear spatial discretzation methods have been developed for the linear Boltzmann transport equation. One known as the first-flux (FF) method [11]. The AF method of these is the highly accurate nonlinear corner-balance (NLCB) is defined by a nonlinear system of equations with two method, which yields a strictly positive solution. Because the disparts: (i) the transport equation and (ii) low-order equacrete NLCB scheme is algebraically nonlinear, special iterative methtions. The low-order equations are derived by integrating ods are needed to solve it efficiently. In this paper, we describe a fast new iterative algorithm, based on the nonlinear averaged flux the transport equation over certain intervals of the angular method, for solving the discrete NLCB equations. We present nuvariable. The resulting system of angle-independent equamerical results that illustrate the efficiency of the new algorithm. tions is closed by special linear-fractional functionals that ᮊ 1997 Academic Press are weakly dependent on the transport solution. The stability of these functionals with respect to the variation of the solution during iterations yields high convergence rates. 66