Graduate Thesis Or Dissertation
 

Accelerating the convergence of the k-eigenvalue problem using a coarse mesh finite differencing scheme in cylindrical geometry

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  • Reactor modeling is largely limited by the computational time required to perform accurate full core calculations. There are many different methods and techniques employed in different reactor simulation codes, but properly modeling all of the physics that takes place in the system requires extensive computational effort. The Coarse Mesh Finite Differencing (CMFD) technique was proposed in 1983 by Kord Smith as a spatial acceleration scheme to combat this problem. It is a nonlinear iterative method that reduces the storage requirement of the problem by reducing the number of unknowns in the system. It is a diffusion based method that can be applied to diffusion and transport problems. The macroscopic cross sections and diffusion coefficients are homogenized accordingly to a coarser mesh. The reaction rates in the new coarse mesh cells are preserved along with the higher order surface currents. A current correction coefficient is introduced to maintain these currents. The finite differencing numerical approximation can then be applied to the 3-Dimensional steady-state neutron diffusion equation resulting in a linear system of equations that is readily solvable. This project has involved implementing the CMFD Acceleration into the reactor simulation code PARCS. PARCS was developed jointly between Purdue University and the University of Michigan to model Pebble Bed Modular Reactors. Although PARCS contains numerous numerical techniques, the focus of this research has been to accelerate the Fine Mesh Finite Differencing approximation in cylindrical geometry. Cylindrical coordinates prevents a higher order nodal method from being used as the primary scheme, but it allows for a more accurate representation of the core. The CMFDA was employed using a 2 group cross section library for fast and thermal neutrons.
  • Keywords: Acceleration, CMFD, PARCS
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