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，改进和应用新的格子玻尔兹曼方法（LBM）的可压缩流。尽管LBM在弱可压缩流的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框架来模拟热和完全耦合的可压缩流，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性效应方面的优缺点的理解。缺乏对重现这些影响的方法的详细分析。首先，LBM模型必须是能量守恒的，当采用完全可压缩流时，标准LBM公式不能满足这一要求。其次，速度集必须适合于高速流动和宽的温度范围，由大量具有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，对流步的离散化对方法的灵活性起着决定性的作用。标准格式的缺点是固定的时间步长和用于速度离散化的巨大的速度集，因为这些速度集必须与笛卡尔网格匹配并遵守形状的对称性。最近，提出了两种非常有前途的方法。第一种是Frapolli等人的称为熵LBM（ELBM）的方法，代表了可压缩流的格点LBM求解器。我们的项目将比较ELBM我们最近开发的方法，代表一个非格插值为基础的半拉格朗日LBM求解器（SLLBM）。它代表了一个新的广义制定的LBM，允许有效的模拟不规则网格。我们的新方法的优点包括域的几何灵活性，高阶平流步骤，可变的时间步长和复杂的速度集容易应用。这些优点将使SLLBM成为模拟热和可压缩流的高潜力候选者。继ELBM和SLLBM在本建议的第一部分中的实质性分析，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的模拟在该项目的第二部分中进行，部分是第一次与可压缩LBM一般。这是必要的，以分析在各自的方法的差异，并获得所需的见解，找到一个公认的和建立的方法，可压缩流使用LBM。测试用例允许调查内禀和变密度压缩性效应分别，包括激波，甚至允许（各向同性湍流）分裂成螺线管和螺旋形的部分，除了与文献的详细比较。