Discrete unified gas kinetic scheme for steady multiscale neutron transport

Abstract

A discrete unified gas kinetic schemes (DUGKS) is developed to solve the steady multidimensional and multigroup neutron transport problems based on the Boltzmann equation. Compared with the traditional neutron transport methods, this steady DUGKS (SDUGKS) has the asymptotic preserving properties and can give good numerical predictions for multiscale transport ranging from optically thin to optically thick regimes (diffusive limit). In the SDUGKS a delta-form-based discrete ordinate (SN) framework is adopted to solve the steady Boltzmann transport equation. But unlike the direct interpolation in the traditional numerical methods for neutron transport, the interface angular fluxes are obtained by integrating the steady Boltzmann equation along the neutron transport direction. The traditional step schemes or other robust schemes can be adopted to discretize the increment to ensure numerical stability. Based on the above special treatments, the sweeping and iterative strategies of the new developed SDUGKS are completely the same as those of the traditional steady SN methods, and thus SDUGKS can be easily implemented in the existing SN transport codes, only by adding the residuals into the source terms. Several numerical tests are performed and the numerical solutions show that the results of the present SDUGKS agree well with the reference solutions for problems with different values of optical thickness, which indicates the advantages of the developed SDUGKS over the conventional methods. Overall, the SDUGKS can serve as a potential numerical tool for multiscale neutron transport problems covering a wide range of optical thickness.