Consistent models for large eddy simulation on anisotropic grids

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Turbulence is an important phenomenon in many natural and man-made systems. Our ability to make accurate predictions of turbulent flows is important in a wide range of scientific and engineering disciplines, including atmospheric flows, aerospace, naval, automotive, wind and nuclear energy, etc. In all these fields, we rely on supercomputers to 'simulate' turbulence in order to predict tomorrow's weather, the lift and drag of a future airplane design, and so on. These types of turbulence simulations solve a set of mathematical equations on a grid of smaller cells. In the vast majority of applications, these cells are anisotropic, i.e., they have different lengths in different directions. In contrast, the vast majority of the underlying mathematical and physical theory upon which these turbulence simulations are based was developed for the assumption of isotropic (i.e., perfectly cubic) cells. This project is aimed at reconciling this gap, which is expected to lead to more accurate and trustworthy turbulence simulations across the wide range of disciplines in which they are used.The goal of this project is to develop models for turbulence-resolving simulations (mainly, large eddy simulations) that behave consistently and accurately on anisotropic grids. Consistency is defined here as having the right behavior in the limits of increasing anisotropies, while accuracy is defined as making effective and efficient use of the given grid resolution. Models of both eddy-viscosity and tensorial forms will be considered. A key component of the project is to perform a comprehensive and conclusive assessment of how different grid anisotropies affect the accuracy, and to communicate this to developers and practitioners in the field. This should raise awareness and hopefully stimulate further work throughout the field, beyond the planned model developments in the present project. The assessment will be performed on multiple canonical flows, including channel flow, a temporally developing mixing layer, and a transitional boundary layer. Crucially, the assessment will be performed using three different numerical codes, to ensure the robustness of the findings and avoid code-specific conclusions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.