A Variational P1 -DP0 Diffusion Theory for Planar Geometry
Conference
·
OSTI ID:15006002
A variational analysis is used to derive a mixed P{sub 1}DP{sub 0} (spherical harmonics-double spherical harmonics) angular approximation to the time-independent monoenergetic neutron transport equation with linearly anisotropic scattering in one-dimensional planar geometry. This mixed approximation contains a space-dependent weight factor {alpha}(x) that controls the local angular approximation used: {alpha}(x) = 1 yields the standard P{sub 1} (diffusion) approximation, {alpha}(x) = 0 gives the standard DP{sub 0} approximation, and 0 < {alpha}(x) < 1 produces a mixed approximation. The diffusion equation obtained differs from the standard P{sub 1} diffusion equation only in the definition of the diffusion coefficient. The variational analysis shows that both the scalar flux and the current are continuous at material interfaces regardless of the value of {alpha}(x). Standard Marshak boundary conditions are also obtained via the variational analysis. In this paper, they examine the use of this mixed angular approximation to more accurately treat material interfaces and vacuum boundaries. Numerical results from a mixed-oxide fuel test problem are presented to demonstrate that significant improvements in accuracy can be obtained using this method. For this test problem, the mixed P{sub 1}-DP{sub 0} angular approximation with {alpha} = 0.25 is found to be more robust than the standard DP{sub 0} approximation ({alpha} = 0) for treating the material interfaces and vacuum boundaries.
- Research Organization:
- Lawrence Livermore National Lab., CA (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 15006002
- Report Number(s):
- UCRL-JC-150125
- Country of Publication:
- United States
- Language:
- English
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