Finite element approximation to the even-parity transport equation
The finite element method is a procedure for reducing partial differential equations to sets of simultaneous algebraic equations suitable for solution on a digital computer. In addressing neutron transport systems, two approahces have been taken, one using discrete ordinates approximations to the conventional form of the transport equation. The second, developed here uses a variational principle as a point of departure for the application of finite elements to neutron transport problems. To formulate finite element methods variational y, the within-group transport equation first is cast into the second-order form that is even parity in angle. The resulting equation is self-adjoint, and may be expressed as a variational principle; the even-parity transport equation is the Euler-Lagrange equation that results from minimizing a corresponding functional. Finite element approximations are than forms of the Ritz procedure provided that the trial functions are continuous in space. Because the dependent variable is the even-parity flux components, and one-half the conventional number of unknowns is required for a given level of angular approximations. Applications to a variety of transport problem classes is analyzed in succeeding sections inlcuding fine mesh multigroup computational procedures and coarse mesh methods.
- Research Organization:
- Northwestern Univ., Evanston, IL
- OSTI ID:
- 6935906
- Journal Information:
- Adv. Nucl. Sci. Technol.; (United States), Journal Name: Adv. Nucl. Sci. Technol.; (United States) Vol. 13; ISSN ANUTA
- Country of Publication:
- United States
- Language:
- English
Similar Records
The variational nodal method: A three-dimensional transport method in Cartesian, triangular, and hexagonal geometries
Buckled spherical harmonics solutions of neutron transport problems
Related Subjects
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CALCULATION METHODS
COMPUTER CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
NEUTRAL-PARTICLE TRANSPORT
NEUTRON TRANSPORT
NUMERICAL SOLUTION
RADIATION TRANSPORT