An Integral Form of the Variational Nodal Method

Journal Article · Sun Feb 15 04:00:00 EST 2004 · Nuclear Science and Engineering

OSTI ID:20804910

Smith, M A ^[1]; Palmiotti, G ^[1]; Lewis, E E ^[2]; Tsoulfanidis, N ^[3]

---

1. Argonne National Laboratory (United States)
2. Northwestern University (United States)
3. University of Missouri, Rolla (United States)

An integral form of the variational nodal method is formulated, implemented, and tested. The method combines an integral transport treatment of the even-parity flux within the spatial node with an odd-parity spherical harmonics expansion of the Lagrange multipliers at the node interfaces. The response matrices that result from this formulation are compatible with those in the VARIANT code at Argonne National Laboratory. Spatial discretization within each node allows for accurate treatment of homogeneous or heterogeneous node geometries. The integral method is implemented in Cartesian x-y geometry and applied to three benchmark problems. The method's accuracy is compared to that of the standard spherical harmonic formulation of the variational nodal method, and the CPU and memory requirements of the two approaches are compared and contrasted. In general, for calculations requiring higher-order angular approximations, the integral method yields solutions with comparable accuracy while requiring substantially less CPU time and memory than the spherical harmonics approach.

• OSTI ID: 20804910
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 2 Vol. 146; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BENCHMARKS
GEOMETRY
INTEGRALS
MATHEMATICAL SOLUTIONS
SERIES EXPANSION
SPHERICAL HARMONICS
VARIATIONAL METHODS