Reactor core analysis through the SP3-ACMFD approach Part II: Transient solution

In this part, an implicit time dependent solution is presented for the Boltzmann transport equation discretized by the analytic coarse mesh finite difference method (ACMFD) over the spatial domain as well as the simplified P₃ (SP₃) for the angular variable. In the first part of this work we proposed a SP₃-ACMFD approach to solve the static eigenvalue equations which provide the initial conditions for temp dependent equations. Having solved the 3D multi-group SP₃-ACMFD static equations, an implicit approach is resorted to ensure stability of time steps. An exponential behavior is assumed in transverse integrated equations to establish a relationship between flux moments and currents. Also, analytic integration is benefited for the time-dependent solution of precursor concentration equations. Finally, a multi-channel one-phase thermal hydraulic model is coupled to the proposed methodology. Transient equations are then solved at each step using the GMRES technique. To show the sufficiency of proposed transient SP₃-ACMFD approximation for a full core analysis, a comparison is made using transport peers as the reference. To further demonstrate superiority, results are compared with a 3D multi-group transient diffusion solver developed as a byproduct of this work. Outcomes confirm that the idea can be considered as an economic interim approach which is superior to the diffusion approximation, and comparable with transport in results.