Adaptive Large Eddy Simulation and Reduced-Order Modeling

The quality of large eddy simulations can be substantially improved through optimizing the positions of the grid points. LES-specific spatial coordinates are computed using a dynamic mesh moving PDE defined by means of physically motivated design criteria such as equidistributed resolution of turbulent kinetic energy and shear stresses. This moving mesh approach is applied to a three-dimensional flow over periodic hills at Re=10,595 and the numerical results are compared to a highly resolved LES reference solution. Further, the applicability of reduced-order techniques to the context of large eddy simulations is explored. A Galerkin projection of the incompressible Navier--Stokes equations with Smagorinsky sub-grid filtering on a set of reduced basis functions is used to obtain a reduced-order model that contains the dynamics of the LES. As an alternative method, a reduced-order model of the un-filtered equations is calibrated to a set of LES solutions. Both approaches are tested with POD and CVT modes as underlying reduced basis functions