Closed-form solution of the first-order Transport-Driven Diffusion approximation

Paolo Picca; Roberto Furfaro

doi:10.1016/j.anucene.2014.10.016

Closed-form solution of the first-order Transport-Driven Diffusion approximation

Paolo Picca, Roberto Furfaro

Systems and Industrial Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

The paper presents a closed-form solution of the first-order Transport-Driven Diffusion (TDD) proposed by Picca and Furfaro (2014). The solution is rigorously derived for two source configurations (i.e. Dirac's delta and rectangular source) to explicitly describe the contribution of the uncollided component and the collided diffuse term. The results are employed to compare the solution of first-order Transport-Driven Diffusion (TDD_T with T = 1) with the analytical diffusion approximation as well as to validate numerical solution of the TDD₁. The comparison with higher-order TDD (i.e., (TDD_T with T > 1) is also reported.

Original language	English (US)
Pages (from-to)	431-438
Number of pages	8
Journal	Annals of Nuclear Energy
Volume	76
DOIs	https://doi.org/10.1016/j.anucene.2014.10.016
State	Published - Feb 2015

Keywords

Closed-form solution
Diffusion theory
Neutral particle transport
Transport-Driven Diffusion

ASJC Scopus subject areas

Nuclear Energy and Engineering

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10.1016/j.anucene.2014.10.016

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title = "Closed-form solution of the first-order Transport-Driven Diffusion approximation",

abstract = "The paper presents a closed-form solution of the first-order Transport-Driven Diffusion (TDD) proposed by Picca and Furfaro (2014). The solution is rigorously derived for two source configurations (i.e. Dirac's delta and rectangular source) to explicitly describe the contribution of the uncollided component and the collided diffuse term. The results are employed to compare the solution of first-order Transport-Driven Diffusion (TDDT with T = 1) with the analytical diffusion approximation as well as to validate numerical solution of the TDD1. The comparison with higher-order TDD (i.e., (TDDT with T > 1) is also reported.",

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AU - Picca, Paolo

AU - Furfaro, Roberto

PY - 2015/2

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N2 - The paper presents a closed-form solution of the first-order Transport-Driven Diffusion (TDD) proposed by Picca and Furfaro (2014). The solution is rigorously derived for two source configurations (i.e. Dirac's delta and rectangular source) to explicitly describe the contribution of the uncollided component and the collided diffuse term. The results are employed to compare the solution of first-order Transport-Driven Diffusion (TDDT with T = 1) with the analytical diffusion approximation as well as to validate numerical solution of the TDD1. The comparison with higher-order TDD (i.e., (TDDT with T > 1) is also reported.

AB - The paper presents a closed-form solution of the first-order Transport-Driven Diffusion (TDD) proposed by Picca and Furfaro (2014). The solution is rigorously derived for two source configurations (i.e. Dirac's delta and rectangular source) to explicitly describe the contribution of the uncollided component and the collided diffuse term. The results are employed to compare the solution of first-order Transport-Driven Diffusion (TDDT with T = 1) with the analytical diffusion approximation as well as to validate numerical solution of the TDD1. The comparison with higher-order TDD (i.e., (TDDT with T > 1) is also reported.

KW - Closed-form solution

KW - Diffusion theory

KW - Neutral particle transport

KW - Transport-Driven Diffusion

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DO - 10.1016/j.anucene.2014.10.016

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EP - 438

JO - Annals of Nuclear Energy

JF - Annals of Nuclear Energy

ER -

Closed-form solution of the first-order Transport-Driven Diffusion approximation

Abstract

Keywords

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