Department of Mathematics

Applied Mathematics

  •  Ming Tse Paul Laiu, Oak Ridge National Laboratory
  •  A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
  •  12/07/2018
  •  4:10 PM - 5:00 PM
  •  1502 Engineering Building

We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on well-known benchmark problems and gives promising results.

 

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