Nonlinear methods for solving particle transport problems

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Abstract
The paper deals with nonlinear numerical methods for solving the transport equation. The Quasi-Diffusion method and nonlinear flux methods are considered. Two approaches to discretization of the considered method equations are compared. Consistent and independent difference schemes are considered. The described nonlinear methods are analyzed to formulate conditions on difference schemes that guarantee satisfying the small scattering limit, the diffusion limit, and the balance equation by a numerical solution. It is shown that in some curvilinear geometry transport problems a small parameter at the highest derivative arises in the moment equations of the nonlinear flux methods. Convergence rates of iteration processes of considered methods are compared. An idea for deriving a nonlinear monotone difference scheme for the multidimensional transport equation is proposed.

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