scholarly journals Neutron angular flux reconstruction in slab geometry using multigroup discrete ordinates transport models

2021 ◽  
Vol 8 (3A) ◽  
Author(s):  
Hermes Alves Filho
Keyword(s):  
Neutron Transport ◽  
Isotropic Scattering ◽  
Computational Time ◽  
Discrete Ordinates ◽  
Neutron Transport Equation ◽  
Slab Geometry ◽  
Neutron Shielding ◽  
Integral Term ◽  
Spatial Domains ◽  
Neutron Propagation

In this article, we present an application of the coarse-mesh Deterministic Spectral Method (SDM) to generate multigroup angular fluxes in one-dimensional spatial domains using the neutron transport stationary equation, in the formulation of discrete ordinates (SN), considering isotropic scattering source. After obtaining the analytical solution of the SN equations, we replace the integral term of the scattering source in the original neutron transport equation. Thus, we obtain analytically two expressions for angular fluxes in the multigroup formulation, considering the neutron propagation in the positive ( ) and negative ( ) directions, presenting a meaningful reduction in the computational time of simulations of typical neutron shielding problems.

Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

2002 ◽  
Author(s):  
Ruben Panta Pazos ◽  
Marco Tullio de Vilhena ◽  
Eliete Biasotto Hauser
Keyword(s):  
Transport Equation ◽  
Truncation Error ◽  
Neutron Transport ◽  
Discrete Ordinates ◽  
Angular Variable ◽  
Two Dimensional ◽  
Neutron Transport Equation ◽  
Discrete Approximations ◽  
Integral Term ◽  
The Laplace Transform

In the last decade Vilhena and coworkers10 reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional SN equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTSN method9, which consists in the application of the Laplace transform to the set of nodal SN equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of SN up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal SN equations for N up to 16 and we begin the convergence of the SN nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation6.

scholarly journals Spectral-Nodal Deterministic Methodology for Neutron Shielding Calculations using the X, Y - geometry Multigroup Transport Equation in the Discrete Ordinates Formulation

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Amaury Munoz Oliva ◽  
Hermes Alves Filho
Keyword(s):  
Neutron Transport ◽  
Numerical Results ◽  
Isotropic Scattering ◽  
Discrete Ordinates ◽  
Reactor Physics ◽  
Neutron Shielding ◽  
Nodal Method ◽  
Fine Mesh ◽  
Mesh Method ◽  
Neutron Transport Equations

In this work, we present the most recent numerical results in a nodal approach, which resulted in the development of a new numerical spectral nodal method, based on the spectral analysis of the multigroup, isotropic scattering neutron transport equations in the discrete ordinates ($S_N$) formulation for fixed-source calculations in non-multiplying media (shielding problems). The numerical results refer to simulations of typical problems from the reactor physics field, in rectangular two-dimensional Cartesian geometry, $X, Y$ geometry, and are compared with the traditional Diamond Difference ($DD$) fine-mesh method results, used as a reference, and the spectral coarse-mesh method Green's function ($SGF$) results.

Variational Approach in Transport Theory

2004 ◽  
Author(s):  
Rube´n Panta Pazos ◽  
Marco Tu´llio de Vilhena
Keyword(s):  
Variational Approach ◽  
Transport Theory ◽  
Neutron Transport ◽  
Specular Reflection ◽  
Adjoint Equations ◽  
Discrete Ordinates ◽  
Neutron Transport Equation ◽  
Bounded Set ◽  
Transport Problems ◽  
Complementary Subset

In this work we present a variational approach to some methods to solve transport problems of neutral particles. We consider a convex domain X (for example the geometry of slab, or a convex set in the plane, or a convex bounded set in the space) and we use discrete ordinates quadrature to get a system of differential equations derived from the neutron transport equation. The boundary conditions are vacuum for a subset of the boundary, and of specular reflection for the complementary subset of the boundary. Recently some different approximation methods have been presented to solve these transport problems. We introduce in this work the adjoint equations and the conjugate functions obtained by means of the variational approach. First we consider the general formulation, and then some numerical methods such as spherical harmonics and spectral collocation method.

Sign in / Sign up

Export Citation Format

Share Document