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Consistent Algorithms Marching Along Characteristics for the Numerical Solution of the Boltzmann Equation
Joint Authors
Nunes, Rogerio C.
Roberty, Nilson C.
Source
Journal of Applied Mathematics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-04-06
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
We introduce algorithms marching over a polygonal mesh with elements consistent with the propagation directions of the particle (radiation) flux.
The decision for adopting this kind of mesh to solve the one-speed Boltzmann transport equation is due to characteristics of the domain of the transport operator which controls derivatives only in the direction of propagation of the particles (radiation) flux in the absorbing and scattering media.
This a priori adaptivity has the advantages that it formulates a consistent scheme which makes appropriate the application of the Lax equivalence theorem framework to the problem.
In this work, we present the main functional spaces involved in the formalism and a description of the algorithms for the mesh generation and the transport equation solution.
Some numerical examples related to the solution of a transmission problem in a high-contrast model with absorption and scattering are presented.
Also, a comparison with benchmarks problems for source and reactor criticality simulations shows the compatibility between calculations with the algorithms proposed here and theoretical results.
American Psychological Association (APA)
Roberty, Nilson C.& Nunes, Rogerio C.. 2011. Consistent Algorithms Marching Along Characteristics for the Numerical Solution of the Boltzmann Equation. Journal of Applied Mathematics،Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-447693
Modern Language Association (MLA)
Roberty, Nilson C.& Nunes, Rogerio C.. Consistent Algorithms Marching Along Characteristics for the Numerical Solution of the Boltzmann Equation. Journal of Applied Mathematics No. 2011 (2011), pp.1-26.
https://search.emarefa.net/detail/BIM-447693
American Medical Association (AMA)
Roberty, Nilson C.& Nunes, Rogerio C.. Consistent Algorithms Marching Along Characteristics for the Numerical Solution of the Boltzmann Equation. Journal of Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-447693
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447693