Finite Element Solution of the Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

Journal Article · Fri Nov 15 04:00:00 EST 2002 · Nuclear Science and Engineering

OSTI ID:20804818

Liscum-Powell, Jennifer L ^[1]; Prinja, Anil B ^[2]; Morel, Jim E ^[3]; Lorence, Leonard J Jr ^[1]

---

1. Sandia National Laboratories (United States)
2. University of New Mexico (United States)
3. Los Alamos National Laboratory (United States)

A novel approach is proposed for charged particle transport calculations using a recently developed second-order, self-adjoint angular flux (SAAF) form of the Boltzmann transport equation with continuous slowing-down. A finite element discretization that is linear continuous in space and linear discontinuous (LD) in energy is described and implemented in a one-dimensional, planar geometry, multigroup, discrete ordinates code for charged particle transport. The cross-section generating code CEPXS is used to generate the electron and photon transport cross sections employed in this code. The discrete ordinates SAAF transport equation is solved using source iteration in conjunction with an inner iteration acceleration scheme and an outer iteration acceleration scheme. Outer iterations are required with the LD energy discretization scheme because the two angular flux unknowns within each group are coupled, which gives rise to effective upscattering. The inner iteration convergence is accelerated using diffusion synthetic acceleration, and the outer iteration convergence is accelerated using a diamond difference approximation to the LD energy discretization. Computational results are given that demonstrate the effectiveness of our convergence acceleration schemes and the accuracy of our discretized SAAF equation.

• OSTI ID: 20804818
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 3 Vol. 142; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCELERATION
ACCURACY
APPROXIMATIONS
BOLTZMANN EQUATION
CHARGED-PARTICLE TRANSPORT
CROSS SECTIONS
DIAMONDS
DISCRETE ORDINATE METHOD
ELECTRONS
FINITE ELEMENT METHOD
ONE-DIMENSIONAL CALCULATIONS
PHOTON TRANSPORT
SLOWING-DOWN
TRANSPORT THEORY