Efficient Pin Level Core Transient Simulation Employing Simplified P3 Method with Multi-Level CMFD Acceleration

In order to efficiently simulate a reactor core using three-dimensional (3D) simplified P3 (SP3) equations, a methodology called direct calculation with multilevel CMFD acceleration is developed. In this methodology, the 3D problem is decomposed into multiple pin-wise one-dimensional (1D) finite difference method (FDM) problems along the axial direction. Since the problem of 1D FDM can be solved directly by the forward/backward substitution, the feasible performance in terms of computing time is achieved with limited resources. Also, with axially fine mesh structure, the fission distribution along the axial direction is more accurately calculated. The direct calculation is then coupled with two levels of 3D coarse mesh finite difference (CMFD) acceleration. The first one is the application of pin level CMFD acceleration based on SP3 equations. It has a plane-wise axially coarse mesh structure and introduces the diffusion correction factor along the axial direction in order to balance the neutron current with the 1D direct calculation. The main purposes of this local CMFD include generating the high order pin level solution based on SP3 and providing the transverse leakage source along the radial direction to the 1D calculation, which resolve the instability problem often reported in 2D/1D scheme. Due to the pin-wise coupling between 1D and 3D calculations, the newly developed methodology is also called 3D/1D scheme. Furthermore, assembly-wise 3D CMFD acceleration based on the diffusion theory is also employed in order to accelerate the convergence of the entire solution globally. In this study, numerical results considering both time independent and dependent cases verify the outstanding performance of the developed 3D/1D scheme. For the steady state condition, following outcomes are obtained; first, the scheme has a convergence behavior with great stability verified through solving small reactor problems where the limitation of the 2D/1D is starkly shown. Second, 3D/1D scheme achieves practical performance in terms of the computing time as efficient as 2D/1D scheme. In third, the scheme provides agreeable results with the reference solution generated from the fine mesh 3D, or so-called direct whole FDM calculation. Furthermore, the characteristics of the 3D/1D are also consistent in the transient core simulation. The sufficiently accurate results are obtained from the scheme, which are comparable to the referential FDM calculation for every transient time step, but with reduced average computing time for each step. With this, the results successfully demonstrate that the newly developed 3D/1D scheme based on SP3 equations performs the pin level core analysis with great efficiency and accuracy