Abstract
SummaryThe accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the underresolved regime, mass conservation and energy stability are key ingredients to obtain robust and accurate discretisations. Recently, two approaches have been proposed in the context of high‐order discontinuous Galerkin (DG) discretisations that address these aspects differently. On the one hand, standard L2‐based DG discretisations enforce mass conservation and energy stability weakly by the use of additional stabilisation terms. On the other hand, pointwise divergence‐free H(div)‐conforming approaches ensure exact mass conservation and energy stability by the use of tailored finite element function spaces. This work raises the question whether and to which extent these two approaches are equivalent when applied to underresolved turbulent flows. This comparative study highlights similarities and differences of these two approaches. The numerical results emphasise that both discretisation strategies are promising for underresolved simulations of turbulent flows due to their inherent dissipation mechanisms.
Highlights
1.1 MotivationSimulating turbulent flows is still a challenging undertaking, even on today’s high-performance computing architectures
Discontinuous Galerkin (DG) discretisations are currently investigated in order to develop new discretisation methods with inbuilt stabilisation mechanism rendering these methods robust and accurate when applied to turbulent flow problems
While the two ‘extreme cases’ of direct numerical simulation (DNS) on the one hand, and Reynolds-averaged Navier–Stokes (RANS) simulations on the other hand are relatively well-established and well-understood, being able to perform time-dependent turbulent flow simulations with only a limited amount of fine-scale accuracy usually goes by the name large-eddy simulation (LES)
Summary
Simulating turbulent flows is still a challenging undertaking, even on today’s high-performance computing architectures. Discontinuous Galerkin (DG) discretisations are currently investigated in order to develop new discretisation methods with inbuilt stabilisation mechanism rendering these methods robust and accurate when applied to turbulent flow problems In this contribution, we compare the accuracy of two high-order DG solvers for incompressible flows with a special emphasis on how they perform in the practically relevant situation of only being able to marginally resolve the occurring flow features. While the two ‘extreme cases’ of direct numerical simulation (DNS) on the one hand, and Reynolds-averaged Navier–Stokes (RANS) simulations on the other hand are relatively well-established and well-understood, being able to perform time-dependent turbulent flow simulations with only a limited amount of fine-scale accuracy usually goes by the name large-eddy simulation (LES) This regime is exactly where we are interested in in this work. The numerical results for the (div)-conforming method have been obtained using NGSolve 22, the results for the 2-based DG using the open-source finite element library deal.II 23
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