Nonlinear Weighted Flux Methods for Particle Transport Problems in 2d Cartesian Geometry
نویسندگان
چکیده
The family of nonlinear weighted flux methods for solving the transport equation is derived for 2D Cartesian geometry. A linear polynomial weight is considered. An asymptotic diffusion limit analysis is performed on the discretized method. The analysis reveals conditions on the weight necessary for an accurate approximation of the diffusion equation. As a result, we developed a new weighted flux method, the equations of which give rise to the diffusion equation in optically thick diffusive regions. Numerical results are presented to confirm the theoretical results and demonstrate performance of the proposed method.
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