Development and analysis of implicit subgrid-scale modeling strategies within a grid-based Eulerian discretization and a grid-less Lagrangian discretization. Application and comparison of these strategies for complex turbulent flows

基于网格的欧拉离散化和无网格拉格朗日离散化中隐式亚网格尺度建模策略的开发和分析。

• 批准号: 5405053
• 负责人: Professor Dr.-Ing. Nikolaus Andreas Adams
• 金额: --
• 依托单位: Lehrstuhl für Aerodynamik und Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5405053?language=en
• 关键词: Development; analysis; implicit; subgrid; scale

Further development of large-eddy simulation faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyses indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS-model. Relevant discretizations are finite-volume schemes with a nonlinear regularization to maintain nonlinear stability and particle methods where a smoothed reconstruction of the particle velocity from the vorticity field is used. Both methods, the grid-based finite-volume method and the mesh-less particle method, have their specific advantages and disadvantages. In this project we investigate both approaches in parallel. For the finite-volume approach, an adaptive approximate deconvolution is introduced for the reconstruction of cell-face data from the cell-averaged solution. Given a properly selected numerical flux function the numerical truncation error and thus the resulting implicit SGS model can be controlled. Formulation and analysis of implicit SGS-model for the two-dimensional particle method are available. In this project we extend this approach to three space dimensions. For an improved accuracy of the implicit SGS-model an approximate deconvolution will be employed. As deliverables after the application period a grid-based finite-volume method and a grid-less particle method for the efficient solution of complex turbulent incompressible flows will be available with the potential for ready extension to compressible flows. Based on mathematical and computational analysis, classes of flows for which each of these methods delivers high accuracy are defined.

大涡模拟的进一步发展面临的主要障碍是亚网格尺度（SGS）模型和数值离散截断误差之间的强耦合。最近的分析表明，对于某些离散和某些流动配置的截断误差本身可以作为隐式SGS模型。相关的离散化是有限体积计划与非线性正则化，以保持非线性稳定性和粒子的方法，其中使用的粒子速度从涡量场的平滑重建。基于网格的有限体积法和无网格粒子法这两种方法各有优缺点。在这个项目中，我们将同时研究这两种方法。对于有限体积法，引入了一种自适应近似反卷积，用于从单元平均解重建单元面数据。只要适当选择数值通量函数，数值截断误差和由此得到的隐式SGS模型就可以得到控制。给出了二维质点法的隐式SGS模型的公式和分析。在这个项目中，我们将这种方法扩展到三维空间。为了提高隐式SGS模型的精度，将采用近似反卷积。作为应用期后的交付成果，用于复杂湍流不可压缩流的有效解的基于网格的有限体积法和无网格粒子法将具有扩展到可压缩流的潜力。基于数学和计算分析，定义了这些方法中的每一种提供高精度的流类。