{"title":"非平衡扩散模型的两组辐射转移基准","authors":"R. McClarren","doi":"10.1080/23324309.2022.2032757","DOIUrl":null,"url":null,"abstract":"Abstract Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model\",\"authors\":\"R. McClarren\",\"doi\":\"10.1080/23324309.2022.2032757\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.\",\"PeriodicalId\":54305,\"journal\":{\"name\":\"Journal of Computational and Theoretical Transport\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-02-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Theoretical Transport\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/23324309.2022.2032757\",\"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/10.1080/23324309.2022.2032757","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}
Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model
Abstract Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.
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.