H¹ Approximations of the Neutron Transport Equation and Associated Diffusion Equations

Abstract

In this article, we give H¹ approximations of the neutron transport equation based on variational formulations of the transport equation recently presented in Bourhrara (2004). These approximations are solutions of some variational problems on H¹. We also show that the strong formulation of one of these approximate problems is no other than the classical neutron diffusion equation, taking into account the transport imposed incoming flux and the albedo boundary conditions. We also give an error estimate between the angular and the scalar flux of the transport equation and the H¹ approximations.

Keywords:

• Neutron transport
• Diffusion equation
• Variational problem
• Approximation

Acknowledgments

I thank Richard Sanchez for his encouragements during the drafting of the present article.