Mixed-hybrid discretization methods for the P-1 equations

作者：Van Criekingen S^*; Beauwens R

来源：Applied Numerical Mathematics, 2007, 57(2): 117-130.

DOI：10.1016/j.apnum.2006.01.004

• mixed-hybrid discretization methods
• linear Boltzmann transport equation
• P-1 approximation

We consider mixed-hybrid discretization methods for the linear Boltzmann transport equation which is extensively used in computational neutron transport. Mixed-hybrid methods combine attractive features of both mixed and hybrid methods, namely the simultaneous approximation of the flux and current, and the use of Lagrange multipliers to enforce interface regularity constraints.
In the present contribution, we cover the case of the P-1 equations which represent the simplest approximation to the Boltzmann equation still retaining typical transport features. This constitutes a necessary preliminary step for the study of the general P-N equations.
We prove the well-posedness of the mixed-hybrid discretization method for the P-1 equations in the dual formulation. A similar proof applies to the primal formulation. This approach generalizes similar results formerly obtained by Babuska et al. for the primal formulation of the diffusion equation. Also, it provides a mathematical basis for various discretization techniques commonly used in nuclear reactor analysis.

• 出版日期2007-2
• 单位中国地震局