diff --git a/Docs/source/refs.bib b/Docs/source/refs.bib index 5c1d27b24a..737461e2eb 100644 --- a/Docs/source/refs.bib +++ b/Docs/source/refs.bib @@ -775,7 +775,6 @@ @article{SHESTAKOV2005 year = "2005", issn = "0022-4073", doi = "https://doi.org/10.1016/j.jqsrt.2004.05.052", -url = "http://www.sciencedirect.com/science/article/pii/S0022407304002092", author = "A.I. Shestakov and J.H. Bolstad", keywords = "Linearized, Multigroup diffusion, Radiation, Transfer, Transport", abstract = "An exact solution, based on Fourier and Laplace (FL) transforms, is developed for a linearization of the system modeling the multifrequency radiation diffusion and matter energy balance equations. The model uses an ideal gas equation of state. Opacities are proportional to the inverse of the cube of the frequency, thereby simulating freeā€“free transitions. The solution is obtained in terms of integrals over the FL coefficients of the initial conditions and explicit sources. Results are presented for two special cases. (1) No sources, initially cold radiation field, and a localized matter energy profile. (2) Initially cold matter and radiation fields and a source of matter energy extending over finite space and time intervals." @@ -830,7 +829,6 @@ @article{suolson:1996 year = "1996", issn = "0022-4073", doi = "https://doi.org/10.1016/0022-4073(96)84524-9", -url = "http://www.sciencedirect.com/science/article/pii/0022407396845249", author = "Su Bingjing and Gordon L. Olson", abstract = "As an extension of previous work in the literature, this paper considers a particular one-dimensional, halfspace, non-equilibrium Marshak wave problem. The radiative transfer model employed is a one-group diffusion approximation with Marshak boundary condition, where the radiation and material fields are out of equilibrium. An analytic solution for the distribution of radiative energy and material temperature as a function of space and time to this problem is given and tables of numerical results are generated. These benchmark results, together with the previously published results, are useful as a reference for validating time-dependent radiation diffusion computer codes. A comparison with a finite difference solution is presented which shows excellent agreement when a fine spatial mesh and small time steps are used." } @@ -844,7 +842,6 @@ @article{suolson:1999 year = "1999", issn = "0022-4073", doi = "https://doi.org/10.1016/S0022-4073(98)00105-8", -url = "http://www.sciencedirect.com/science/article/pii/S0022407398001058", author = "Bingjing Su and Gordon L. Olson", abstract = "Benchmark solutions to time-dependent radiative transfer problems involving non-equilibrium coupling to the material temperature field are crucial for validating time-dependent radiation transport codes. Previous efforts on generating analytical solutions to non-equilibrium radiative transfer problems were all restricted to the one-group grey model. In this paper, a non-grey model, namely the picket-fence model, is considered for a two temperature non-equilibrium radiative transfer problem in an infinite medium. The analytical solutions, as functions of space and time, are constructed in the form of infinite integrals for both the diffusion description and transport description. These expressions are evaluated numerically and the benchmark results are generated. The asymptotic solutions for large and small times are also derived in terms of elementary functions and are compared with the exact results. Comparisons are given between the transport and diffusion solutions and between the grey and non-grey solutions." }