2 edition of **Finite element solution of the multigroup transport equation in two-dimensional geometries.** found in the catalog.

Finite element solution of the multigroup transport equation in two-dimensional geometries.

Juhani PitkaМ€ranta

- 307 Want to read
- 30 Currently reading

Published
**1974**
by The Finnish Academy of Technical Sciences in Helsinki
.

Written in English

**Edition Notes**

Series | Acta Polytechnica Scandinavica : Physics including Nucleonics Series -- No. 101 |

The Physical Object | |
---|---|

Pagination | 33 p., ill |

Number of Pages | 33 |

ID Numbers | |

Open Library | OL21258937M |

ISBN 10 | 9516660363 |

The standard Galerkin finite element procedure then renders a discrete system of equations for the nodal displacements U of the form (18) where K is the global stiffness matrix, U is the vector of nodal degrees of freedom, F is the global force vector due to external loads, and F d is the image force vector due to the internal dislocation : A. Sheng, N. M. Ghoniem, T. Crosby, G. Po. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite Edition: 1.

KEYWORDS: multigroup, transport equation, two dimensions, r-z geometry, PL approximation, finite difference method, numerical solutions, spherical harmonics method I. INTRODUCTION In many cases, neutron transport equation is solved with a discrete-ordinates method . LEAST-SQUARES FINITE-ELEMENT DISCRETIZATION OF THE NEUTRON TRANSPORT EQUATION IN SPHERICAL GEOMETRY C. KETELSEN, T. MANTEUFFEL, AND J. B. SCHRODERy Abstract. The main focus of this paper is the numerical solution of the Boltzmann transport equation for neutral particles through mixed material media in a spherically symmetric Size: 1MB.

Finite Volume Methods Robert Eymard1, Thierry Gallou¨et2 and Rapha`ele Herbin3 October This manuscript is an update of the preprint n0 du LATP, UMR , Marseille, September which appeared in Handbook of Numerical Analysis, P.G. Ciarlet, J.L. Lions eds, vol 7, pp TRIPLET solves the two-dimensional multigroup transport equation in planar geometries by using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (K/sub eff/ and eigenvalue searches) problems subject to vacuum, reflective, or source boundary conditions .

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The extension of a variational finite-element method of solving the neutron transport equation, to include multigroup-energy dependence in R-Z geometry, is evaluated. The method is implemented in a computer program called by: The finite element method is applied to the spatial variables of multi-group neutron transport equation in the two-dimensional cylindrical (r, z) geometry.

The equation is discretized using regular rectangular subregions in the (r, z) by: 3. Multigroup solutions are based on a maximum principlefor the one-group second-ordereven-parity transport equation. A novel featureof the method is an enumeration scheme for the spherical harmonic moments at the nodes of the finite element network which minimizes the bandwidth of Cited by: The finite element method (FEM) is a widely-used method to solve neutron transport equation in an arbitrary domain, but in order to ensure the accuracy of solution a re-meshing process is often required and some regions of the domain need to be meshed with finer meshes and consequently the whole domain should be re-meshed by: 5.

A variational finite element-spherical harmonics method is presented for the solution of the even-parity multigroup equations with anisotropic scattering and sources. It is shown that by using a simple and natural formulation the numerical implementation of the method for any desired geometry is greatly eased and the anisotropy of scatter Cited by: The extension of the theory of a multigroup finite-element method of solving the neutron transport equation, to include general anisotropy of scattering and an anisotropic spatially-dependent source, is described.

Pergamon Journals Ltd A MULTIGROUP FINITE-ELEMENT SOLUTION OF THE NEUTRON TRANSPORT EQUATION--Ill ANISOTROPY OF SCATTERING Cited by: 6. Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures.

In this paper, the solution of multigroup forward/adjoint equation. The neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid.

This work introduces the alternatives that unstructured grids can provide Cited by: 6. Preface This is a set of lecture notes on ﬁnite elements for the solution of partial differential equations.

The approach taken is mathematical in nature with a strong focus on theFile Size: 2MB. Request PDF | ENTRANS: A platform for finite elements modeling of 3D neutron transport equation, Part II. Multidimensional implementation | Practical challenges concerning the solution of multi.

A popular and widely used approach to the solution of partial diﬀerential equations is the ﬁnite element method (FEM), which, as often in numerical mathematics, reduces the initial problem to the task of solving a system of linear equations.

For this pur-pose, especially when dealing with a large number of unknowns (e.g. ∼ ), classical. Contents 1. 2D weak form (based on the principle of virtual work) 2. 2D finite element method (based on the weak form) Learning outcome A. Understanding of the main principles behind the 2D finite element method B.

Ability to formulate and apply the finite element method for 2D model problems References Lecture notes: chapters −6, −4 Text book: chapters −4. Discrete ordinate neutron transport equation for two-dimensional triangular mesh is investigated by Reed'1 ', and TRIPLET code''' is developed by using the finite element method for the space variable.

In these discrete ordinate equations derived by the finite. Combined finite volume and finite element method for convection-diffusion-reaction equation Article (PDF Available) in Journal of Mechanical Science and Technology 23(3) March with.

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.

Discrete formulation for two-dimensional multigroup neutron diffusion equations Article in Annals of Nuclear Energy 31(3) January with 48 Reads How we measure 'reads'. FINITE ELEMENT METHODS FOR THE TRANSPORT EQUATION by P. LESAINT (*) Communiqué par P.-A. RAVIART. Abstract.

Finite element methods for solving the two dimensional x y transport équation are considered and some practical numerical schemes are defined. A particular empiasis is put upon the bounds for the errors due to the spatial by: 4. ONETRAN solves the one-dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries.

Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux. Lesaint and P. Raviart, On a finite element method for solving the neutron transport problems, C.

de Boor, editor, Mathematical aspects of finite elements in partial differential equations. The finite element method is the most widely used method for solving problems of engineering and mathematical models. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.

The FEM is a particular numerical method for solving partial differential equations in two or three space variables. To solve a problem, the FEM. Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous Cited by: 2.Abstract.

Finite element methods for problems of neutron transport have been an academic field of activity for over a decade. Reviews of the state of the art have been given by Williams and Goddard (1) and Lewis (2) and a short history of the finite element method in various fields given by Ackroyd (3).Cited by: General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted.

TWODANT numerically solves the two-dimensional multigroup form of the neutral-particle, steady-state Boltzmann transport equation.