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

进一步发展大涡模拟的主要障碍是次网格尺度(SGS)模式与数值离散截断误差之间的强耦合。最近的分析表明，对于某些离散化和某些流动形态，截断误差本身可以作为隐式SGS模型。相关的离散化方法是使用非线性正则化的有限体积格式来保持非线性稳定性，以及粒子方法，其中使用了从涡量场平滑重建粒子速度的方法。基于网格的有限体积法和无网格质点法都有各自的优缺点。在这个项目中，我们并行地研究这两种方法。对于有限体积方法，引入了一种自适应近似反卷积方法，用于从单元平均解重建单元表面数据。在给定适当的数值通量函数的情况下，数值截断误差和由此产生的隐式SGS模型是可以控制的。建立和分析了二维质点方法的隐式SGS模型。在这个项目中，我们将这种方法扩展到三个空间维度。为了提高隐式SGS模型的精度，将采用近似反卷积。作为应用期结束后的成果，基于网格的有限体积方法和用于有效求解复杂湍流不可压缩流动的无网格质点方法将是可用的，并有可能扩展到可压缩流动。基于数学和计算分析，定义了这些方法中的每种方法都能提供高精度的流动类别。

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.