東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Hybrid Discrete (HTN) Approximations...

Shin, Minwoo.

Linked to FindBook

Google Book

Amazon

博客來

Hybrid Discrete (HTN) Approximations to the Equation of Radiative Transfer.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hybrid Discrete (HTN) Approximations to the Equation of Radiative Transfer./
Author:	Shin, Minwoo.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	118 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Contained By:	Dissertations Abstracts International80-12B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13426815
ISBN:	9781392265871

Hybrid Discrete (HTN) Approximations to the Equation of Radiative Transfer.
Shin, Minwoo.

Hybrid Discrete (HTN) Approximations to the Equation of Radiative Transfer. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 118 p.

Source: Dissertations Abstracts International, Volume: 80-12, Section: B.

Thesis (Ph.D.)--Iowa State University, 2019.

This item must not be sold to any third party vendors.

The linear kinetic transport equations are ubiquitous in many application areas, including as a model for neutron transport in nuclear reactors and the propagation of electromagnetic radiation in astrophysics. The main computational challenge in solving the linear transport equations is that solutions live in a high-dimensional phase space that must be sufficiently resolved for accurate simulations. The three standard computational techniques for solving the linear transport equations are the (1) implicit Monte Carlo, (2) discrete ordinate (SN), and (3) spherical harmonic (PN) methods. Monte Carlo methods are stochastic methods for solving time-dependent nonlinear radiative transfer problems. In a traditional Monte Carlo method when photons are absorbed, they are reemitted in a distribution which is uniform over the entire spatial cell where the temperature is assumed constant, resulting in loss of information. In implicit Monte Carlo(IMC) methods, photons are reemitted from the place where they were actually absorbed, which improves the accuracy. Overall, IMC method improves stability, flexibility, and computational efficiency fleck. The SN method solves the transport equation using a quadrature rule to reconstruct the energy density. This method suffers from so-called "ray effect", which are due to the approximation of the double integral over a unit sphere by a finite number of discrete angular directions chai. The PN approximation is based on expanding the part of the solution that depends on velocity direction (i.e., two angular variables) into spherical harmonics. A big challenge with the PN approach is that the spherical harmonics expansion does not prevent the formation of negative particle concentrations. The idea behind my research is to develop on an alternative formulation of PN approximations that hybridizes aspects of both PN and SN. Although the basic scheme does not guarantee positivity of the solution, the new formulation allows for the introduction of local limiters that can be used to enforce positivity.

ISBN: 9781392265871Subjects--Topical Terms:

1669109
Applied Mathematics.

Hybrid Discrete (HTN) Approximations to the Equation of Radiative Transfer.
LDR:03108nmm a2200313 4500 001 2208024
005 20190929184031.5
008 201008s2019 ||||||||||||||||| ||eng d
020 $a 9781392265871
035 $a (MiAaPQ)AAI13426815
035 $a (MiAaPQ)iastate:17805
035 $a AAI13426815
040 $a MiAaPQ $c MiAaPQ
100 1 $a Shin, Minwoo. $3 3435032
245 1 0 $a Hybrid Discrete (HTN) Approximations to the Equation of Radiative Transfer.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 118 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Rossmanith, James A.
502 $a Thesis (Ph.D.)--Iowa State University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a The linear kinetic transport equations are ubiquitous in many application areas, including as a model for neutron transport in nuclear reactors and the propagation of electromagnetic radiation in astrophysics. The main computational challenge in solving the linear transport equations is that solutions live in a high-dimensional phase space that must be sufficiently resolved for accurate simulations. The three standard computational techniques for solving the linear transport equations are the (1) implicit Monte Carlo, (2) discrete ordinate (SN), and (3) spherical harmonic (PN) methods. Monte Carlo methods are stochastic methods for solving time-dependent nonlinear radiative transfer problems. In a traditional Monte Carlo method when photons are absorbed, they are reemitted in a distribution which is uniform over the entire spatial cell where the temperature is assumed constant, resulting in loss of information. In implicit Monte Carlo(IMC) methods, photons are reemitted from the place where they were actually absorbed, which improves the accuracy. Overall, IMC method improves stability, flexibility, and computational efficiency fleck. The SN method solves the transport equation using a quadrature rule to reconstruct the energy density. This method suffers from so-called "ray effect", which are due to the approximation of the double integral over a unit sphere by a finite number of discrete angular directions chai. The PN approximation is based on expanding the part of the solution that depends on velocity direction (i.e., two angular variables) into spherical harmonics. A big challenge with the PN approach is that the spherical harmonics expansion does not prevent the formation of negative particle concentrations. The idea behind my research is to develop on an alternative formulation of PN approximations that hybridizes aspects of both PN and SN. Although the basic scheme does not guarantee positivity of the solution, the new formulation allows for the introduction of local limiters that can be used to enforce positivity.
590 $a School code: 0097.
650 4 $a Applied Mathematics. $3 1669109
690 $a 0364
710 2 $a Iowa State University. $b Mathematics. $3 1266625
773 0 $t Dissertations Abstracts International $g 80-12B.
790 $a 0097
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13426815