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A physically consistent weakly compressible high-resolution approach to underresolved simulations of incompressible flows

Abstract

In engineering applications critical complex unsteady flows often are, at least in certain flow areas, only marginally resolved. Within these areas, the truncation error of the underlying difference schemes strongly affects the solution. Therefore, a significant gain in computational efficiency is possible if the truncation error functions as physically consistent, i.e. reproducing the correct evolution of resolved scales, subgrid-scale (SGS) model. The truncation error of high-order WENO-based schemes can be exploited to function as an implicit subgrid-scale (SGS) model. A recently developed sixth-order adaptive central-upwind weighted essentially non-oscillatory scheme with implicit scale-separation has been demonstrated to incorporate a physically consistent implicit SGS model for compressible turbulent flows. We consider the implicit SGS modeling capabilities of an improved version of this scheme simultaneously for underresolved turbulent and non-turbulent incompressible flows, thus extending previous works on this subject to a more general scope. With this model we are able to reach very long integration times for the incompressible Taylor–Green vortex at infinite Reynolds number, and recover in particular a low-mode transition to isotropy. Inviscid shear-layer instabilities are resolved to highly nonlinear stages, which is shown by considering the doubly periodic two-dimensional shear layer as test configuration. Proper resolved-scale prediction is also obtained for viscous–inviscid interactions and fully confined viscous flows. These properties are demonstrated by applying the model to a vortex–wall interaction problem and lid-driven cavity flow.

Keywords

  • Weakly compressible model;
  • High resolution scheme;
  • Implicit large-eddy simulation;
  • Physically consistent;
  • Underresolved computation

 

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