超越矩：计算天体物理学中辐射输运的相对论性格子玻尔兹曼方法
Beyond moments: relativistic Lattice-Boltzmann methods for radiative transport in computational astrophysics
摘要：
我们提出了一种新的方法，在计算天体物理学中经常遇到的多维场景中的辐射传输方程（RTE）的数值解。该方法是基于玻尔兹曼方程的直接解决方案，通过扩展的格子玻尔兹曼（LB）方程，并允许模拟辐射场的演变，因为它与背景流体相互作用，通过吸收，发射和散射。作为这种方法的第一个应用程序，我们限制我们的注意力频率独立（“灰色”）制定一个特殊的相对论框架内，这也可以用于经典的计算天体物理学。对于一些标准的测试，考虑在光学薄，光学厚和中间制度的静态流体的方法的性能，我们显示的LB方法产生准确和收敛的结果匹配的解析解的能力。我们还对比LB方法与常用的矩为基础的计划的解决方案的RTE，如M1计划。通过这种方式，我们能够强调LB方法为非平凡的自由流场景和中间光学深度区域提供了正确的解决方案，M1方法失败或提供不准确的解决方案。当耦合到一个动态的流体，另一方面，我们提出了第一个自洽的解决方案的RTE与LB方法在相对论流体动力学的情况下。最后，我们表明，除了提供更准确的结果，在所有制度，LB方法具有较小的或可比的计算成本相比，M1计划。
英文摘要：
We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann equation via an extension of the Lattice Boltzmann (LB) equation and allows to model the evolution of the radiation field as it interacts with a background fluid, via absorption, emission, and scattering. As a first application of this method, we restrict our attention to a frequency independent ("grey") formulation within a special-relativistic framework, which can be employed also for classical computational astrophysics. For a number of standard tests that consider the performance of the method in optically thin, optically thick and intermediate regimes with a static fluid, we show the ability of the LB method to produce accurate and convergent results matching the analytic solutions. We also contrast the LB method with commonly employed moment-based schemes for the solution of the RTE, such as the M1 scheme. In this way, we are able to highlight that the LB method provides the correct solution for both non-trivial free-streaming scenarios and the intermediate optical-depth regime, for which the M1 method either fails or provides inaccurate solutions. When coupling to a dynamical fluid, on the other hand, we present the first self-consistent solution of the RTE with LB methods within a relativistic-hydrodynamic scenario. Finally, we show that besides providing more accurate results in all regimes, the LB method features smaller or comparable computational costs compared to the M1 scheme.
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