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

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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.