490
Views
46
CrossRef citations to date
0
Altmetric
Original Articles

Theoretical Aspects of the Simplified Pn Equations

Pages 73-109 | Received 17 Jun 2010, Accepted 10 Oct 2010, Published online: 13 Jan 2011

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (7)

M. R. A. Abdelmalik, Z. Cai & T. Pichard. (2023) On the Renormalization Maps for the φ-Divergence Moment Closures Applied in Radiative Transfer. Journal of Computational and Theoretical Transport 52:6, pages 399-428.
Read now
Zoltán István Böröczki, Boglárka Babcsány, János Endre Maróti & Máté Szieberth. (2023) On the Effect of Scalar Flux Weighting of Linearly Anisotropic Scattering Matrices in Higher-Order Transport Calculations. Nuclear Science and Engineering 197:8, pages 1545-1563.
Read now
Alexander Jesser, Kai Krycki & Martin Frank. (2022) Partial Cross-Section Calculations for PGNAA Based on a Deterministic Neutron Transport Solver. Nuclear Technology 208:7, pages 1114-1123.
Read now
Chao Fang, Liangzhi Cao, Hongchun Wu & Kang Li. (2022) A Residual-Based Subgrid-Scale Method Combined with Spherical Harmonics Angular Approximation for Solving the Boltzmann Transport Equation. Nuclear Science and Engineering 196:5, pages 526-543.
Read now
Michael G. Jarrett, Brendan M. Kochunas, Edward W. Larsen & Thomas J. Downar. (2020) SP3 Limit of the 2D/1D Transport Equations with Varying Degrees of Angular Coupling. Journal of Computational and Theoretical Transport 49:6, pages 303-330.
Read now
I. Makine, R. Vasques & R. N. Slaybaugh. (2018) Exact Transport Representations of the Classical and Nonclassical Simplified PN Equations. Journal of Computational and Theoretical Transport 47:4-6, pages 326-349.
Read now
Jian Cai, Shenghui Lei, Adhiraj Dasgupta, Michael F. Modest & Daniel C. Haworth. (2014) High fidelity radiative heat transfer models for high-pressure laminar hydrogen–air diffusion flames. Combustion Theory and Modelling 18:6, pages 607-626.
Read now

Articles from other publishers (39)

M. Nazari, A. Zolfaghari & M. Abbasi. (2024) Time-dependent simplified approximation for neutron transport equation . Progress in Nuclear Energy 168, pages 105043.
Crossref
Y. Fontenla, A. Vidal-Ferràndiz, A. Carreño, D. Ginestar & G. Verdú. (2024) FEMFFUSION and its verification using the C5G7 benchmark. Annals of Nuclear Energy 196, pages 110239.
Crossref
M. Nazari, A. Zolfaghari & M. Abbasi. (2023) Simplified- treatment of the neutron transport equation . Progress in Nuclear Energy 166, pages 104933.
Crossref
Abhishek Mishra, Aditi Ray & Tej Singh. (2023) Multigroup form of simplified spherical harmonics (SPN) equations for neutron transport. Nuclear and Particle Physics Proceedings 341, pages 81-83.
Crossref
M.R.A. Abdelmalik, Z. Cai & T. Pichard. (2023) Moment methods for the radiative transfer equation based on -divergences . Computer Methods in Applied Mechanics and Engineering 417, pages 116454.
Crossref
Christophe Buet, Bruno Despres & Guillaume Morel. (2023) Approximation Properties of Vectorial Exponential Functions. Communications on Applied Mathematics and Computation.
Crossref
Jonas Kusch, Benjamin Whewell, Ryan McClarren & Martin Frank. (2022) A low-rank power iteration scheme for neutron transport criticality problems. Journal of Computational Physics 470, pages 111587.
Crossref
Abhishek Mishra, Aditi Ray & Tej Singh. (2022) On Simplified Spherical Harmonics (SPN) and Generalized SPN (GSPN) formulations. Annals of Nuclear Energy 173, pages 109071.
Crossref
A. Carreño, A. Vidal-Ferràndiz, D. Ginestar & G. Verdú. (2022) Frequency-domain models in the SP approximation for neutron noise calculations . Progress in Nuclear Energy 148, pages 104233.
Crossref
Michael F. Modest & Sandip Mazumder. 2022. Radiative Heat Transfer. Radiative Heat Transfer 513 561 .
A. Carreño, A. Vidal-Ferràndiz, D. Ginestar & G. Verdú. (2021) Time-dependent simplified spherical harmonics formulations for a nuclear reactor system. Nuclear Engineering and Technology 53:12, pages 3861-3878.
Crossref
Zhuogang Peng & Ryan G. McClarren. (2021) A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations. Journal of Computational Physics 447, pages 110672.
Crossref
M.A. Ramírez-Cabrera & P.J. Valades-Pelayo. (2021) The first-Order scattering method . Journal of Quantitative Spectroscopy and Radiative Transfer 270, pages 107701.
Crossref
Hongkai Zhao & Yimin Zhong. (2021) Quantitative PAT with simplified P N approximation . Inverse Problems 37:5, pages 055009.
Crossref
Mohamed Ghattassi & Takéo Takahashi. (2021) On the null-controllability of a radiative heat transfer system. European Journal of Control 59, pages 143-151.
Crossref
Yuchao Xu, Jason Hou & Kostadin N. Ivanov. (2021) IMPROVEMENT TO NEM SP3 MODELLING AND SIMULATION. EPJ Web of Conferences 247, pages 03008.
Crossref
Boglárka Babcsány & Dániel Péter Kis. (2020) Semi-analytical methods for SP3 equations solver verification including third-order scattering anisotropy. Annals of Nuclear Energy 148, pages 107671.
Crossref
M.T. Capilla, C.F. Talavera, D. Ginestar & G. Verdú. (2020) Validation of the SHNC time-dependent transport code based on the spherical harmonics method for complex nuclear fuel assemblies. Journal of Computational and Applied Mathematics 375, pages 112814.
Crossref
V. Giusti & B. Montagnini. (2020) On the relevance of the scattering anisotropy for a low order transport method. Annals of Nuclear Energy 145, pages 107604.
Crossref
Christophe Demazière. 2020. Modelling of Nuclear Reactor Multi-physics. Modelling of Nuclear Reactor Multi-physics 193 250 .
Richard Sanchez. (2019) On SP theory. Annals of Nuclear Energy 129, pages 331-349.
Crossref
Ehsan Edjlali & Yves Bérubé-Lauzière. (2018) Solving analytically the simplified spherical harmonics equations in cylindrical turbid media. Journal of the Optical Society of America A 35:9, pages 1633.
Crossref
Pan Qingquan, Lu Haoliang, Li Dongsheng & Wang Kan. (2018) The Differences Between the Two Forms of Semi-Analytical Nodal Methods on Solving the Third-Order Simplified Spherical Harmonics Method Equations1. Journal of Nuclear Engineering and Radiation Science 4:2.
Crossref
Mohammad Hasan Jalili Bahabadi, Ali Pazirandeh & Mitra Athari. (2016) Analytic function expansion nodal (AFEN) method for solving multigroup neutron simplified P3 (SP3) equations in hexagonal-z geometry. Annals of Nuclear Energy 98, pages 74-80.
Crossref
Yung-An Chao. (2016) A new and rigorous SP N theory for piecewise homogeneous regions. Annals of Nuclear Energy 96, pages 112-125.
Crossref
Richard Vasques. (2016) The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation. Applied Mathematics Letters 53, pages 63-68.
Crossref
Steven P. Hamilton & Thomas M. Evans. (2015) Efficient solution of the simplified equations . Journal of Computational Physics 284, pages 155-170.
Crossref
Mohammad Hasan Jalili Bahabadi, Ali Pazirandeh & Mitra Athari. (2015) New analytic function expansion nodal (AFEN) method for solving multigroup neutron simplified P 3 (SP 3 ) equations. Annals of Nuclear Energy 77, pages 148-160.
Crossref
Martin Frank, Kai Krycki, Edward W. Larsen & Richard Vasques. (2015) The Nonclassical Boltzmann Equation and DIffusion-Based Approximations to the Boltzmann Equation. SIAM Journal on Applied Mathematics 75:3, pages 1329-1345.
Crossref
Zekeriya Altaç. (2014) On radiative transfer using synthetic kernel and simplified spherical harmonics methods in linearly anisotropically scattering media. Journal of Quantitative Spectroscopy and Radiative Transfer 147, pages 8-23.
Crossref
Benjamin Seibold & Martin Frank. (2014) StaRMAP---A Second Order Staggered Grid Method for Spherical Harmonics Moment Equations of Radiative Transfer. ACM Transactions on Mathematical Software 41:1, pages 1-28.
Crossref
Michael F. Modest, Jian Cai, Wenjun Ge & E. Lee. (2014) Elliptic formulation of the Simplified Spherical Harmonics Method in radiative heat transfer. International Journal of Heat and Mass Transfer 76, pages 459-466.
Crossref
M.M.R. Williams, S.K. Hall & M.D. Eaton. (2014) Solution of the two dimensional diffusion and transport equations in a rectangular lattice with an elliptical fuel element using Fourier transform methods: One and two group cases. Annals of Nuclear Energy 63, pages 146-156.
Crossref
V. Giusti, B. Montagnini & P. Ravetto. (2013) Solution of 3D multigroup, linearly anisotropic scattering, criticality problems by the AN boundary-element response-matrix method. Annals of Nuclear Energy 57, pages 350-367.
Crossref
E. Olbrant, E.W. Larsen, M. Frank & B. Seibold. (2013) Asymptotic derivation and numerical investigation of time-dependent simplified equations. Journal of Computational Physics 238, pages 315-336.
Crossref
Michael F Modest. 2013. Radiative Heat Transfer. Radiative Heat Transfer 495 540 .
S. Duerigen & E. Fridman. (2012) The simplified P3 approach on a trigonal geometry of the nodal reactor code DYN3D. Kerntechnik 77:4, pages 226-229.
Crossref
Michael F Modest & Shenghui Lei. (2012) The Simplified Spherical Harmonics Method For Radiative Heat Transfer. Journal of Physics: Conference Series 369, pages 012019.
Crossref
Martin Frank & Benjamin Seibold. (2011) Optimal prediction for radiative transfer: A new perspective on moment closure. Kinetic & Related Models 4:3, pages 717-733.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.