A Nonlinear Diffusion Acceleration Scheme for the S N Transport Equation with Anisotropic Scattering Using the Local Discontinuous Galerkin Method

Le résumé fourni par la source

A nonlinear diffusion acceleration (NDA) scheme is developed to efficiently solve the SN transport equation with anisotropic scattering. The spatial discretization of the high-order transport and low-order diffusion equations is based on the discontinuous Galerkin finite element method. A key innovation of this work is the acceleration of the anisotropic scattering source using the P1 moment obtained from the diffusion equation discretized with the local discontinuous Galerkin (LDG) method. Numerical experiments on one- and two-dimensional problems are conducted to examine the stability and effectiveness of the proposed LDG-based NDA method. The numerical results show that the proposed method is unconditionally stable and significantly accelerates convergence. The total computational time is reduced compared with the conventional NDA method without anisotropic scattering acceleration.

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