Finite volume lattice Boltzmann scheme for neutron/radiative transfer on unstructured mesh

In this paper, we propose a novel finite volume lattice Boltzmann (FV-LB) scheme to simulate the neutron and radiative transfer problems governed by the linear Boltzmann transport equation (BTE). In the derivation of the FV-LB scheme, we utilize a multi-speed lattice Boltzmann model to reduce the linear BTE into a linear discrete velocity Boltzmann equation (DVBE). Considering the computational effectiveness and flexibility in complex geometries, we design a finite volume scheme by using the first order upwind numerical flux and solve the DVBE with the finite volume scheme on a unstructured tetrahedral or triangular mesh. The accuracy of the FV-LB scheme is verified by comparing our results with the benchmark values of three representative problems.