超新星中微子输运IDSA的数学描述、离散化及其与玻尔兹曼方程有限体积格式的比较
A Mathematical Description of the IDSA for Supernova Neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann's Equation
摘要：
本文介绍了中微子输运的Boltzmann方程在核塌缩超新星模型中的应用，并对\emph{Isotropic Diffusion Source Approximation}（IDSA）进行了详细的数学描述。此外，我们提出了一种基于时间分裂和有限体积的简化Boltzmann模型问题的数值处理方法，并修正了IDSA的离散化方法。离散化误差的研究进行了减少玻尔兹曼模型问题和IDSA表明，在这两种情况下的错误是一阶。通过数值算例，对简化模型和IDSA进行了详细的比较和解释。对于该示例，相对于简化的玻尔兹曼模型的IDSA建模误差被数值地确定和定位。
英文摘要：
In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the \emph{Isotropic Diffusion Source Approximation} (IDSA). Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized.
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