Method of solution of the neutron transport equation in multidimensional cartesian geometries using spherical harmonics and spatially orthogonal polynomials

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1981

OSTI ID:6155774

Fenstermacher, T E

The solution of the neutron transport equation has long been a subject of intense interest to nuclear engineers. Present computer codes for the solution of this equation, however, are expensive to run for large, multidimensional problems, and also suffer from computational problems such as the ray effect. A method has been developed which eliminates many of these problems. It consists of transforming the transport equation into a set of linear partial differential equations by the use of spherical harmonics. The problem volume is divided into mesh boxes, and the flux components are approximated within each mesh box by spatially orthogonal quadratic polynomials, which need not be continuous at mesh box interfaces. A variational principle is developed, and used to solve for the unknown coefficients of these polynomials. Both one dimensional and two dimensional computer codes using this method have been written. The codes have each been tested on several test cases, and the solutions checked against solutions obtained by other methods. While the codes have some difficulty in modeling sharp transients, they produce excellent results on problems where the characteristic lengths are many mean free paths. On one test case, the two dimensional code, SHOP/2D, required only one-fourth the computer time required by the finite difference, discrete ordinates code TWOTRAN to produce a solution. In addition, SHOP/2D converged much better than TWOTRAN and produced more physical-appearing results.

• Research Organization: Maryland Univ., College Park (USA)
• OSTI ID: 6155774
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
COMPUTER CALCULATIONS
COMPUTER CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
NEUTRAL-PARTICLE TRANSPORT
NEUTRON TRANSPORT
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
RADIATION TRANSPORT
S CODES
SPHERICAL HARMONICS METHOD
TWO-DIMENSIONAL CALCULATIONS