ColtBig: Compressible and thermal lattice Boltzmann methods on interpolation-based grids

ColtBig：基于插值网格的可压缩和热晶格玻尔兹曼方法

• 批准号: 439383920
• 负责人: Professor Dr.-Ing. Holger Foysi
• 金额: --
• 依托单位: Lehrstuhl für Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/439383920?language=en
• 关键词: ColtBig; Compressible; thermal; lattice; Boltzmann

Our goal is to study, improve, and apply novel lattice Boltzmann methods (LBM) for compressible flows. Despite the widely acknowledged success of LBM for the simulation of weakly compressible flows, an accepted framework for the simulation of thermal and fully coupled compressible flows is still lacking according to the literature, which is due to the large number of possible extensions and a lack of understanding of the strengths and weaknesses of the various approaches in reproducing variable density or intrinsic compressibility effects. A detailed analysis of the approaches to reproduce those effects is lacking. Firstly, the LBM model has to be energy conserving, a requirement not met by the standard LBM formulation when adopted to fully compressible flows. Secondly, the velocity sets have to be suited to high-speed flows and to a broad temperature range, being represented by a large number of energy shells with different particle velocities. Contrary to the standard LBM for weakly compressible flows, velocity sets coinciding with the Cartesian grid mostly do not fulfill these requirements. Lastly, the discretization of the advection step plays a decisive role in the flexibility of the methods. Standard schemes suffer from the fixed time step and from the enormous velocity sets that are used for the velocity discretization, since the sets have to both match the Cartesian grid and to obey symmetry in their shape. Recently, two very promising approaches were presented. The first is by Frapolli et al. called the entropic LBM (ELBM), representing an on-lattice LBM solver for compressible flows. Our project will compare the ELBM to our recently developed approach representing an off-lattice interpolation based semi-Lagrangian LBM solver (SLLBM). It represents a new generalized formulation of the LBM that allows for efficient simulations on irregular grids. Advantages of our new method include the geometric flexibility of the domain, the high-order advection step, a variable time step size and the easy application of sophisticated velocity sets. These advantages will turn the SLLBM into a high-potential candidate for the simulation of thermal and compressible flows. Succeeding a substantial analysis of the ELBM and the SLLBM in the first part of this proposal, simulations of compressible forced isotropic turbulence, compressible temporal mixing layers, and supersonic turbulent channel flows are performed in the second part of the project, partly for the first time with compressible LBM in general. This is necessary to analyze differences in the respective approaches and to gain required insights into finding an accepted and established approach to compressible flows using LBM. The test cases allow investigating intrinsic and variable density compressibility effects seperately, include shocklets and even allow (isotropic turbulence) a splitting into solenoidal and dilatational parts, in addition to a detailed comparison with the literature.

我们的目标是研究、改进和应用用于可压缩流的新型格子玻尔兹曼方法 (LBM)。尽管LBM在弱可压缩流模拟方面取得了广泛的成功，但根据文献，仍然缺乏一个公认的热流和全耦合可压缩流模拟框架，这是由于大量可能的扩展和缺乏了解再现可变密度或固有压缩效应的各种方法的优点和缺点。缺乏对重现这些效果的方法的详细分析。首先，LBM 模型必须是节能的，当采用完全可压缩流时，标准 LBM 公式无法满足这一要求。其次，速度组必须适合高速流动和较宽的温度范围，由大量具有不同粒子速度的能量壳代表。与弱可压缩流的标准 LBM 相反，与笛卡尔网格一致的速度集大多不能满足这些要求。最后，平流步骤的离散化对方法的灵活性起着决定性作用。标准方案受到固定时间步长和用于速度离散化的巨大速度集的影响，因为这些集必须既匹配笛卡尔网格又遵守其形状的对称性。最近，提出了两种非常有前途的方法。第一个是 Frapolli 等人的作品。称为熵 LBM (ELBM)，代表可压缩流的格上 LBM 求解器。我们的项目将把 ELBM 与我们最近开发的代表基于离格插值的半拉格朗日 LBM 求解器 (SLLBM) 的方法进行比较。它代表了 LBM 的一种新的广义公式，可以在不规则网格上进行有效的模拟。我们的新方法的优点包括域的几何灵活性、高阶平流步骤、可变时间步长以及复杂速度集的易于应用。这些优点将使 SLLBM 成为热流和可压缩流模拟的高潜力候选者。继本提案第一部分对 ELBM 和 SLLBM 进行实质性分析之后，该项目的第二部分首次对可压缩强迫各向同性湍流、可压缩时间混合层和超音速湍流通道流进行了模拟一般情况下使用可压缩的 LBM。这对于分析各个方法的差异以及获得所需的见解以找到使用 LBM 的可压缩流的公认且既定的方法是必要的。除了与文献进行详细比较之外，测试用例还允许分别研究固有和变密度压缩性效应，包括冲击波，甚至允许（各向同性湍流）分裂为螺线管和膨胀部分。