{"title":"无限介质的基准,具有各向同性散射的时间相关输运问题","authors":"W. Bennett, R. McClarren","doi":"10.1080/23324309.2022.2103151","DOIUrl":null,"url":null,"abstract":"Abstract The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green’s functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green’s functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Benchmarks for Infinite Medium, Time Dependent Transport Problems with Isotropic Scattering\",\"authors\":\"W. Bennett, R. McClarren\",\"doi\":\"10.1080/23324309.2022.2103151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green’s functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green’s functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.\",\"PeriodicalId\":54305,\"journal\":{\"name\":\"Journal of Computational and Theoretical Transport\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Theoretical Transport\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/23324309.2022.2103151\",\"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/10.1080/23324309.2022.2103151","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}
Benchmarks for Infinite Medium, Time Dependent Transport Problems with Isotropic Scattering
Abstract The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green’s functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green’s functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.
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.