Improvement of variational nodal transport methods by Lagrange multiplier techniques

Conference · Thu Jan 01 04:00:00 EST 1987 · Trans. Am. Nucl. Soc.; (United States)

OSTI ID:6892937

Lewis, E E

It has been demonstrated in earlier work that nodal transport methods can be formulated through the use of a variational form of the even-parity transport equation. The resulting methods have been used to obtain coarse-mesh solutions to two-dimensional P/sub 1/ and P/sub 3/ equations in a response matrix form. The formalism preserves neutron balance in each spatial node, while allowing the flux distribution within a node to be treated as a complete polynomial or other finite element like trial function. Subsequently, the method has been formulated as a global functional in which the odd-parity interface conditions appear as Lagrange multipliers. It is shown that the Lagrange multiplier formulation may be used to reduce the number of basis functions used to specify the interface conditions, thereby reducing the dimension of the nodal response matrices without a commensurate loss of accuracy. Specifically, by careful choice of Lagrange multiplier trial functions, one can cut the number of interface conditions by two and still obtain near P/sub 3/ accuracy. Moreover, the resulting formalism suffers neither from ray effects nor from the inaccuracies for streaming diagonal to the coordinate directions that have been observed in some nodal transport methods.

• Research Organization: Argonne National Lab., IL (USA)
• OSTI ID: 6892937
• Report Number(s): CONF-8711195-
• Conference Information: Journal Name: Trans. Am. Nucl. Soc.; (United States) Journal Volume: 55
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
LAGRANGE EQUATIONS
NEUTRAL-PARTICLE TRANSPORT
NEUTRON FLUX
NEUTRON TRANSPORT
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
RADIATION FLUX
RADIATION TRANSPORT
TWO-DIMENSIONAL CALCULATIONS