Abstract
PROTEUS-MOC is a pin-resolved high-fidelity transport code, in which the axial variation of angular flux is represented in terms of orthogonal polynomials. Currently, PROTEUS-MOC employs linear functions and requires relatively fine axial meshes to achieve high accuracy, which increases the number of axial meshes and hence the memory requirement. In this study, aiming to reduce the memory requirement and potentially the computational time by allowing larger axial meshes, we have extended the PROTEUS-MOC transport solution method to quadratic trial functions. Preliminary tests for the performance of quadratic trial functions have been performed using the 3-D C5G7 benchmark problem. Test results showed that for the same axial mesh configuration with relatively large sizes, the quadratic approximation yields about 2 to 5 times more accurate pin powers than the linear approximation, depending on the degree of axial variation of angular fluxes. The quadratic approximation also allows the use of about 3 times coarser axial meshes than the linear approximation for comparable pin power accuracy, which consequently reduces the memory requirement by about 2 times. The memory reduction is not proportional because of the increased number of coefficients in each element from 2 to 3. However, the quadratic approximation did not reduce the computational time as expected because of the deteriorated performance of the pCMFD acceleration scheme due to large axial mesh sizes.
Highlights
Three-dimensional (3-D) heterogeneous whole-core deterministic transport calculation is gaining increasing interest due to its capability to provide high-fidelity, pin-resolved flux solutions
In this study, aiming to reduce the memory requirement and potentially the computational time by allowing larger axial meshes, we have extended the PROTEUS-method of characteristics (MOC) transport solution method to quadratic trial functions
The mean relative error (MRE) error of segment 3 is 0.08% and comparable to that of segment 1 or 2, suggesting that all the relatively large pin-segment power errors in segment 3 occurred in the fuel pins of relatively small powers. These results indicate that the quadratic approximation allows using about 3 times coarser axial meshes than the linear approximation for comparable pin-segment power accuracy
Summary
Three-dimensional (3-D) heterogeneous whole-core deterministic transport calculation is gaining increasing interest due to its capability to provide high-fidelity, pin-resolved flux solutions. PROTEUS-MOC solves the first-order Boltzmann transport equation for axially extruded geometries of 2-D unstructured meshes by combining MOC for the radial direction and the discontinuous Galerkin finite element method (DFEM) in the axial direction. It provides a fully consistent and accurate solution of the 3-D transport equation by overcoming the limitations of the 2-D/1-D method without any noticeable increase in computational time. By the use of the Galerkin weighted residual technique, a system of 2-D partial differential equations for the expansion coefficients is obtained for each axial slice This system of equations has a similar form to the 2-D transport equation, and it can be solved using a 2-D MOC solver with exponentials of matrices instead of numbers.
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