Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport

Applications of the transient Boltzmann transport equation (BTE) have undergone much investigation, such as radiative heat transfer and neutron transport. This paper provides a lattice Boltzmann model to efficiently resolve the multidimensional transient BTE. For a higher angular resolution, enough transport directions are considered while the transient BTE in each direction is treated as a conservation law equation and solved independently. Both macroscopic equations recovered from a Chapman-Enskog expansion and simulated results of typical benchmark problems show not only the second-order accuracy but also the flexibility and applicability of the proposed lattice Boltzmann model. This approach may contribute a powerful technique for the parallel simulation of large-scale engineering and some alternative perspectives for solving the nonlinear transport problem further.

Figure 1

Schematic of (a) azimuthal angle $\theta$, latitudinal angle $\phi$, and (b) discrete solid angle.

Figure 2

Scheme of two-dimensional mesh configuration for lattice Boltzmann model.

Figure 3

Schematic of boundary node $B$ and its adjacent node $O$.

Figure 4

Schematic of (a) one-dimensional slab with (b) short square-pulse laser.

Figure 5

Comparisons of (a) transmittance and (b) reflectance between proposed LBM and FVM [61].

Figure 6

Schematic of two-dimensional plane with incident pulse.

Figure 7

Comparisons of (a) transmittance and (b) reflectance between proposed LBM and MCM [29].

Figure 8

Schematic of two-dimensional plane for steady-state neutron transport problem.

Figure 9

Scalar flux (a) along the diagonal and the distribution of scalar flux for (b) $\omega =0$, (c) $\omega =0.5$, and (d) $\omega =0.75$.