Abstract
In this work we investigate the interplay of polynomial de-aliasing and
sub-grid scale models for large eddy simulations based on discontinuous
Galerkin discretizations. It is known that stability is a major concern
when simulating underresolved turbulent flows with high order nodal
collocation type discretizations. By changing the interpolatory
character of the nodal collocation type discretization to a projection
based discretization by increasing the number of quadrature points
(polynomial de-aliasing), one is able to remove the aliasing induced
stability problems. We focus on this effect and on the consequence for
large eddy simulations with explicit subgrid scale models. Often,
subgrid scale models have to achieve two possibly conflicting tasks in a
single simulation: firstly stabilizing the numerics and secondly
modeling the physical effect of the missing scales. Within a
discontinuous Galerkin approach, it is possible to use either a fast
(but potentially aliasing afflicted) nodal collocation discretization or
a projection-based (but computationally costly) variant in combination
with an explicit subgrid scale model. We use this framework to
investigate the effect on the appropriate model parameter of a standard
Smagorinsky subgrid scale model and of a Variational Multiscale
Smagorinsky formulation. For this we first consider the 3-D viscous
Taylor-Green vortex example to investigate the impact on the stability
of the method and second the turbulent flow past a circular cylinder to
investigate and compare the accuracy of the results. We show that the
aliasing instabilities of collocative discretizations severely limit the
choice of the model constant, in particular for high order schemes,
while for de-aliased DG schemes, the closure model parameters can be
chosen independently from the numerical scheme. For the cylinder flow,
we also find that for the same model settings, the projection-based
results are in better agreement with the reference DNS than those of the
collocative scheme.
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