发表机构
Indian Institute of Science（印度科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于紧支撑帽函数的玻尔兹曼格式，用于捕获接触间断，简化数值分析并直接证明正性，扩展至二阶精度，在一维和二维基准无粘流问题中验证。
AI 中文摘要
麦克斯韦速度分布函数的适当矩可以恢复气体动力学欧拉方程的守恒变量和通量向量。然而，麦克斯韦分布在速度空间中具有无限支撑，这给基于它的动力学格式的数值分析带来了挑战。尽管麦克斯韦分布是自然选择，但它并不是唯一保持这些关键矩的分布函数。在其开创性论文中，Perthame（1990）引入了一种紧支撑的帽函数作为替代。本文提出了基于 peculiar velocity（ peculiar 速度）构造的、使用帽函数的接触间断捕获玻尔兹曼格式的公式化与分析。由于帽函数在速度空间中的紧支撑性，所提格式的数值分析大大简化，从而可以直接证明其正性。该格式扩展到二阶精度，且不损害其一阶对应格式的正性保持性质，并在多个一维和二维基准无粘流问题中进行了测试。
英文摘要
The suitable moments of the Maxwell velocity distribution function recover the conserved variable and flux vectors of the Euler equations of gas dynamics. However, the Maxwellian has infinite support in velocity space, which poses challenges for the numerical analysis of kinetic schemes based on it. Although Maxwellian is a natural choice, it is not the only distribution function that preserves these key moments. In his seminal paper, Perthame (1990) introduced a compactly supported hat function as an alternative. This paper presents the formulation and analysis of a contact discontinuity capturing Boltzmann scheme based on peculiar velocity, constructed using the hat function. Owing to the compact support of the hat function in velocity space, the numerical analysis of the proposed scheme is considerably simplified, allowing for a direct proof of its positivity. The scheme, extended to second-order accuracy without compromising the positivity-preserving property of its first-order counterpart, is tested on several benchmark inviscid flow problems in one- and two-dimensions.
