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、改进和应用新的晶格玻尔兹曼方法（LBM）来研究可压缩流。尽管LBM在模拟弱可压缩流动方面取得了广泛的成功，但根据文献，仍然缺乏一个可接受的热和完全耦合可压缩流动模拟框架，这是由于大量可能的扩展以及缺乏对各种方法在再现变密度或固有压缩效应方面的优缺点的理解。目前还缺乏对重现这些效应的方法的详细分析。首先，LBM模型必须是节能的，这是标准LBM公式在用于完全可压缩流动时不能满足的要求。其次，速度集必须适合于高速流动和较宽的温度范围，由大量不同粒子速度的能量壳层表示。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满足这些要求。最后，平流阶跃的离散化对方法的灵活性起着决定性的作用。标准方案受到固定时间步长和用于速度离散的巨大速度集的影响，因为这些集必须既匹配笛卡尔网格，又服从其形状的对称性。最近，提出了两种非常有前途的方法。第一个是由Frapolli等人提出的，称为熵LBM (ELBM)，代表了可压缩流的点阵LBM求解器。我们的项目将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。它代表了一种新的广义LBM公式，允许在不规则网格上进行有效的模拟。该方法的优点是域的几何灵活性、高阶平流步长、时间步长可变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。在本文第一部分对ELBM和SLLBM进行了大量分析之后，第二部分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进行了模拟，这在一定程度上是第一次对一般的可压缩LBM进行模拟。这对于分析各自方法之间的差异，并获得必要的见解，以找到使用LBM的可压缩流的公认和既定方法是必要的。除了与文献的详细比较外，测试用例还允许分别研究固有和变密度压缩效应，包括激波，甚至允许（各向同性湍流）分裂为螺线管和膨胀管部分。