TY - GEN

T1 - Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation

AU - Ganapol, Barry D

PY - 2015

Y1 - 2015

N2 - For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

AB - For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

KW - Anisotropic scattering

KW - Convergence acceleration

KW - Diagonalization

KW - Second order ODE

UR - http://www.scopus.com/inward/record.url?scp=84949506489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949506489&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84949506489

T3 - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015

SP - 1327

EP - 1338

BT - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015

PB - American Nuclear Society

T2 - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015

Y2 - 19 April 2015 through 23 April 2015

ER -