Semi-analytical solutions of fractional neutron diffusion models with thermal–hydraulic feedback via computational method

In this work, fast and accurate semi-analytical solutions are presented for the two group space–time fractional neutron diffusion model with thermal–hydraulic feedback using computational method. Throughout a linear combination of the Caputo fractional power series, the fractional residual power series method (FR-PWS) is constructed for temporal calculations. A new computable recurrence relation is introduced to estimate the series coefficients in successive algebraic steps. Additionally, higher order finite different (FD) schemes are spatially employed at the core interior meshes and at the core boundary meshes for spatial discretization. It is proved that using these higher order FD schemes significantly improved the steady state calculations preserving the system complexity. Convergence and stability of the FR-PWS method is discussed. It is proved that the convergence order of the higher order FD schemes with different core divisions equals four while the convergence order with different temporal step sizes of the FR-PWS method is approximately 1-α for 0<α≤1. The proposed method is applied simply to two- and three- dimensional space homogenous benchmarks. Then, the method is tested for heterogeneous benchmark reactors with step, ramp, and sinusoidal reactivities. Finally, the method is applied to solve LRA BWR benchmark reactor including adiabatic heating and Doppler feedback. It is proved that for heterogeneous reactors, the effect of the anomalous subdiffusion diminishes throughout the transient for all types of perturbations.