具有各向异性散射的非经典输运简化PN方程的渐近导数

IF 0.7 4区工程技术 Q3 MATHEMATICS, APPLIED

Journal of Computational and Theoretical Transport Pub Date : 2020-01-16 DOI:10.1080/23324309.2020.1816552

Robert Palmer, R. Vasques

{"title":"具有各向异性散射的非经典输运简化PN方程的渐近导数","authors":"Robert Palmer, R. Vasques","doi":"10.1080/23324309.2020.1816552","DOIUrl":null,"url":null,"abstract":"Abstract In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SPN equations are needed. Nonclassical SPN equations to model isotropic scattering have been derived, and the nonclassical SP1 equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SPN equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP1 equation with anisotropic scattering.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"331 - 348"},"PeriodicalIF":0.7000,"publicationDate":"2020-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1816552","citationCount":"1","resultStr":"{\"title\":\"Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering\",\"authors\":\"Robert Palmer, R. Vasques\",\"doi\":\"10.1080/23324309.2020.1816552\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SPN equations are needed. Nonclassical SPN equations to model isotropic scattering have been derived, and the nonclassical SP1 equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SPN equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP1 equation with anisotropic scattering.\",\"PeriodicalId\":54305,\"journal\":{\"name\":\"Journal of Computational and Theoretical Transport\",\"volume\":\"49 1\",\"pages\":\"331 - 348\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/23324309.2020.1816552\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Theoretical Transport\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/23324309.2020.1816552\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Theoretical Transport","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/23324309.2020.1816552","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

摘要在非经典输运中，自由程长度变量s被建模为自变量，并导出了包含s的非经典线性玻尔兹曼输运方程。为了模拟扩散区的输运，已经成功地使用了简化的球谐方程（SPN）。为了模拟扩散区中的非经典输运，需要SPN方程的非经典版本。导出了模拟各向同性散射的非经典SPN方程，并确定了具有各向异性散射的非古典SP1方程，但用于导出该方程的方法无法导出高阶方程。本文提出了一种新的方法，可以导出所有具有各向异性散射的非经典SPN方程。该方法被提出并用于生成这些方程中的第一个，并且它被证明等价于先前导出的具有各向异性散射的非经典SP1方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering

Abstract In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SPN equations are needed. Nonclassical SPN equations to model isotropic scattering have been derived, and the nonclassical SP1 equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SPN equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP1 equation with anisotropic scattering.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Computational and Theoretical Transport Mathematics-Mathematical Physics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Emphasizing computational methods and theoretical studies, this unique journal invites articles on neutral-particle transport, kinetic theory, radiative transfer, charged-particle transport, and macroscopic transport phenomena. In addition, the journal encourages articles on uncertainty quantification related to these fields. Offering a range of information and research methodologies unavailable elsewhere, Journal of Computational and Theoretical Transport brings together closely related mathematical concepts and techniques to encourage a productive, interdisciplinary exchange of ideas.