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Finding the Minimun of the Quadratic Functional in Variational Approach in Transport Theory Problems

[+] Author Affiliations
Rubén Panta Pazos

Universidade de Santa Cruz do Sul, Santa Cruz do Sul, RS, Brazil

Paper No. ICONE16-48479, pp. 835-840; 6 pages
doi:10.1115/ICONE16-48479
From:
  • 16th International Conference on Nuclear Engineering
  • Volume 1: Plant Operations, Maintenance, Installations and Life Cycle; Component Reliability and Materials Issues; Advanced Applications of Nuclear Technology; Codes, Standards, Licensing and Regulatory Issues
  • Orlando, Florida, USA, May 11–15, 2008
  • Conference Sponsors: Nuclear Engineering Division
  • ISBN: 0-7918-4814-0 | eISBN: 0-7918-3820-X
  • Copyright © 2008 by ASME

abstract

In this work it is reviewed the variational approach for some Transport Problems. Let X be a convex domain in Rn , and V a compact set. For that, it is considered the following equation:

∂ψ∂t(x,v,t)+v·∇ψ(x,v,t)+h(x,μ)  ψ(x,v,t)== Vk(x,v,v)ψ(x,v,t)dv  +q(x,v,t) (1)
where x represents the spatial variable in a domain D, v an element of a compact set V, Ψ is the angular flux, h(x,v) the collision frequency, k(x,v,v’) the scattering kernel function and q(x,v) the source function. It is put the attention in the construction of the quadratic functional J which appears in variational approaches for transport theory (for example, the Vladimirov functional). Some properties of this functional in a proper functional framework, in order to determine the minimum for J are considered. First, the general formulation is studied. Then an algorithm is given for minimizing the functional J for two remarkable problems: spherical harmonic method and spectral collocation method. A program associated to this algorithm is worked in a computer algebraic system, and also was depeloped a version in a high level language.

Copyright © 2008 by ASME

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