New Variational Formulations for the Neutron Transport Equation

Abstract

We give in this paper several variational formulations for the neutron transport equation. For each one of these formulations we derive a weak form and show that this form is equivalent to the original transport problem. With the help of Lax‐Milgram's theorem we prove the existence and the uniqueness of the solution in the L ²‐setting. Since the numerical solution of some of these formulations require iterations on the source term, we also prove the convergence of the iterations.

Keywords:

• Transport equation
• Projection method
• Variational formulation

Acknowledgments

I would like to thank R. Sanchez for his help and for fruitful discussions. Among other things, he suggested to me to include formulation 2. I also thank the reviewers for helping to improve the quality of this work.