Leonardo Rodrigues da Costa Moraes

Rio de Janeiro State University | UERJ · Departamento de Modelagem Computacional

We present in this work an extension of the Response Matrix (RM) method for the numerical solution of slab-geometry neutral particle transport equation in the discrete ordinates (SN) and energy multigroup formulations considering non-uniform sources. By using the term non-uniform we mean that the particle source is not spatially uniform inside the...

An improved modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The term “Spectral” is used to indicate that the nonclassical angular flux is approximated as an expansion in terms of spectral basis functions. In the SA the basis functions are the Laguerre...

Described here is the occurrence of linearly dependent eigenvectors in the analytical solution of the spectral approximation of the nonclassical transport equation in the discrete ordinates (SN) formulation. To our knowledge, this characteristic does not arise in the analytical solution of the classical SN transport equations. Therefore, classical...

Presented here is a more general description of the methodology that makes use of the adjoint technique to estimate the neutron source distribution required to drive a subcritical system to a prescribed distribution of power. This methodology is based on a relation between a linear functional with respect to the neutron angular flux and the importa...

In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by...

In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generate...

An improvement modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The main focus of the modified SA lies on a slight modification of the nonclassical angular flux representation as a function of truncated Laguerre series. This leads, in some cases, to a c...

The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle’s free-path. Recently, a spectral approach was developed to generate nonclassical spectral SN equations, which can be numerically solved in a deterministic fashion using classical numerical...

In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generate...

In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by...

The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate nonclassical spectral S$_N$ equations, which can be numerically solved in a deterministic fashion using classical numeric...

Presented here is an application of the Response Matrix (RM†) method for adjoint discrete ordinates (SN) problems in slab-geometry applied to energy-dependent neutral particle transport problems. The RM† method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree wit...

A nuclear system is referred to as subcritical when neutron removal events (leakage through the boundaries of the system and absorption) occur at a rate which is greater than the events that promote the production of these particles (fission). When this occurs the system cannot maintain a stable level of the population of neutrons and tends to shut...

A new approach for the development of a numerical method of spectral nodal class for the solution of multigroup, anisotropic slab geometry, discrete ordinates transport problems with fixed-source is analyzed in this paper. The method, denominated Spectral Deterministic Method (SDM), is based on the spectral analysis of the neutron transport equatio...

This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle transport for random statistically homogeneous systems in which the distribution function for free-paths betwee...

It is well known that any subcritical system can be driven by time-independent interior sources of neutrons. Thus, we present a methodology to determine the intensities of uniform and isotropic sources of neutrons that must be added inside a subcritical system generating a prescribed steady-state distribution of power. To accomplish this, we use th...

We introduce and present a preliminary investigation of P1 and S2 synthetic acceleration for spectral SN equations.

This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle transport for random statistically homogeneous systems in which the distribution function for free-paths betwee...