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In this paper, we derive a method for the second-order form of the transportequation that is both globally conservative and compatible with voids, usingContinuous Finite Element Methods (CFEM). The main idea is to use theLeast-Squares (LS) form of the transport equation in the void regions and theSelf-Adjoint Angular Flux (SAAF) form elsewhere. While the SAAF formulation isglobally conservative, the LS formulation need a correction in void. The priceto pay for this fix is the loss of symmetry of the bilinear form. We firstderive this Conservative LS (CLS) formulation in void. Second we combine theSAAF and CLS forms and end up with an hybrid SAAF-CLS method, having thedesired properties. We show that extending the theory to near-void regions is aminor complication and can be done without affecting the global conservation ofthe scheme. Being angular discretization agnostic, this method can be appliedto both discrete ordinates (SN) and spherical harmonics (PN) methods. However,since a globally conservative and void compatible second-order form alreadyexists for SN (Wang et al. 2014), but is believed to be new for PN, we focusmost of our attention on that latter angular discretization. We implement andtest our method in Rattlesnake within the Multiphysics Object OrientedSimulation Environment (MOOSE) framework. Results comparing it to other methodsare presented.

Globally Conservative, Hybrid Self-Adjoint Angular Flux and Least-Squares Method Compatible with Void