{"title":"线性各向异性散射辐射传递方程的准随机离散坐标法","authors":"P. H. A. Konzen, L. Guidi, T. Richter","doi":"10.4028/p-qWLV5Y","DOIUrl":null,"url":null,"abstract":"The modeling of energy transport via radiative transfer is important to many practical high temperature engineering applications. Furthermore, the computation of solutions to the radiative transfer equation (RTE) plays a fundamental part in it. The quasi-random discrete ordinates method was developed as an alternative to mitigate the ray effect found in the classical discrete ordinates method solutions. The former method was originally developed for transport problems with isotropic scattering and it is here extended and tested to problems with linear anisotropic scattering. Its main idea is to approximate the integral term of the RTE by a quasi-Monte Carlo integration. The discrete system of differential equations arising from it can be solved by a variety of classical discretization methods, here computed with a SUPG finite element scheme. The novel developments are tested for selected manufactured solutions. The achieved good results indicate the potential of the novel method to be applied to the solution of radiative transfer problems with anisotropic scattering.","PeriodicalId":11306,"journal":{"name":"Defect and Diffusion Forum","volume":"427 1","pages":"109 - 119"},"PeriodicalIF":0.0000,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-Random Discrete Ordinates Method to Radiative Transfer Equation with Linear Anisotropic Scattering\",\"authors\":\"P. H. A. Konzen, L. Guidi, T. Richter\",\"doi\":\"10.4028/p-qWLV5Y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The modeling of energy transport via radiative transfer is important to many practical high temperature engineering applications. Furthermore, the computation of solutions to the radiative transfer equation (RTE) plays a fundamental part in it. The quasi-random discrete ordinates method was developed as an alternative to mitigate the ray effect found in the classical discrete ordinates method solutions. The former method was originally developed for transport problems with isotropic scattering and it is here extended and tested to problems with linear anisotropic scattering. Its main idea is to approximate the integral term of the RTE by a quasi-Monte Carlo integration. The discrete system of differential equations arising from it can be solved by a variety of classical discretization methods, here computed with a SUPG finite element scheme. The novel developments are tested for selected manufactured solutions. The achieved good results indicate the potential of the novel method to be applied to the solution of radiative transfer problems with anisotropic scattering.\",\"PeriodicalId\":11306,\"journal\":{\"name\":\"Defect and Diffusion Forum\",\"volume\":\"427 1\",\"pages\":\"109 - 119\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Defect and Diffusion Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4028/p-qWLV5Y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Defect and Diffusion Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4028/p-qWLV5Y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Quasi-Random Discrete Ordinates Method to Radiative Transfer Equation with Linear Anisotropic Scattering
The modeling of energy transport via radiative transfer is important to many practical high temperature engineering applications. Furthermore, the computation of solutions to the radiative transfer equation (RTE) plays a fundamental part in it. The quasi-random discrete ordinates method was developed as an alternative to mitigate the ray effect found in the classical discrete ordinates method solutions. The former method was originally developed for transport problems with isotropic scattering and it is here extended and tested to problems with linear anisotropic scattering. Its main idea is to approximate the integral term of the RTE by a quasi-Monte Carlo integration. The discrete system of differential equations arising from it can be solved by a variety of classical discretization methods, here computed with a SUPG finite element scheme. The novel developments are tested for selected manufactured solutions. The achieved good results indicate the potential of the novel method to be applied to the solution of radiative transfer problems with anisotropic scattering.
期刊介绍:
Defect and Diffusion Forum (formerly Part A of ''''Diffusion and Defect Data'''') is designed for publication of up-to-date scientific research and applied aspects in the area of formation and dissemination of defects in solid materials, including the phenomena of diffusion. In addition to the traditional topic of mass diffusion, the journal is open to papers from the area of heat transfer in solids, liquids and gases, materials and substances. All papers are peer-reviewed and edited. Members of Editorial Boards and Associate Editors are invited to submit papers for publication in “Defect and Diffusion Forum” . Authors retain the right to publish an extended and significantly updated version in another periodical.