Mixed-hybrid discretization methods for the linear Boltzmann transport equation

• Published in: Computer methods in applied mechanics and engineering 2006-04, Vol.195 (19), p.2719-2741
• Main Authors: Van Criekingen, S., Beauwens, R., Jerome, J.W., Lewis, E.E.
• Format: Article
• Language: English
• Subjects: Classical statistical mechanics; Computational techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Kinetic theory; Linear Boltzmann transport equation; Mathematical methods in physics; Mixed-hybrid discretization methods; Physics; PN approximation; Statistical physics, thermodynamics, and nonlinear dynamical systems
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2005.06.002

The linear Boltzmann transport equation is discretized using a finite element technique for the spatial variable and a spherical harmonic technique for the angular variable. With the angular flux decomposed into even- and odd-angular parity components, mixed-hybrid methods are developed that combine the advantages of mixed (simultaneous approximation of even- and odd-parity fluxes) and hybrid (use of Lagrange multipliers to enforce interface regularity conditions) methods. An existence and uniqueness theorem is proved for the resulting problems. Beside the well-known primal/dual distinction induced by the spatial variable, the angular variable leads to an even/odd distinction for the spherical harmonic expansion order.