Andrea Beck

Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method

Scale-resolving simulations of turbulent flows in complex domains demand accurate and efficient numerical schemes, as well as geometrical flexibility. For underresolved situations, the avoidance of aliasing errors is a strong demand for stability. For continuous and discontinuous Galerkin schemes, an effective way to prevent aliasing errors is to increase the quadrature precision of the projection operator to account for the non-linearity of the operands (polynomial dealiasing, overintegration). But this increases the computational costs extensively. In this work, we present a novel spatially and temporally adaptive dealiasing strategy by projection filtering. We show this to be more efficient for underresolved turbulence than the classical overintegration strategy. For this novel approach, we discuss the implementation strategy and the indicator details, show its accuracy and efficiency for a decaying homogeneous isotropic turbulence and the transitional Taylor-Green vortex and compare it to the original overintegration approach and a state of the art variational multi-scale eddy viscosity formulation.

A Discontinuous Galerkin Spectral Element Method for the direct numerical simulation of aeroacoustics

The discontinuous Galerkin Spectral Element Method (DG-SEM) is highly attractive for both DNS and LES of turbulent flows due to its low dispersion and dissipation errors, but also because of its good parallel scaling property. We show that especially for underresolved simulations the method has highly beneficial properties for LES, as well as for the direct treatment of the acoustic propagation. We also discuss different approaches for non-reflecting boundary conditions for DG-SEM and show the behavior of the methods for airfoil flows. Our main intend is to directly simulate trailing edge noise for airfoil flows at medium Reynolds numbers.

An Efficient High Performance Parallelization of a Discontinuous Galerkin Spectral Element Method

We describe an efficient parallelization strategy for the discontinuous Galerkin spectral element method, illustrated by a structured grid framework. Target applications are large scale DNS and LES calculations on massively parallel systems. Due to the simple and efficient formulation of the method, a parallelization aiming at one-element-per-processor calculations is feasible; a highly desired feature for emerging multi- and many-core architectures. We show scale-up tests on up to 131,000 processors.

Discontinuous Galerkin for High Performance Computational Fluid Dynamics (hpcdg)

In this paper we present selected ongoing computations, performed on HLRS clusters. Three efficient explicit Discontinuous Galerkin schemes, suitable for high performance calculations, are employed to perform direct numerical simulations of isotropic turbulence and turbulent channel flow, large eddy simulations of cavity-flows as well as hybrid simulations of aeroacoustic phenomena. The computations were performed on hundreds to thousands computer cores.

High-Order Discontinuous Galerkin Schemes for Large-Eddy Simulations of Moderate Reynolds Number Flows

In this article, we describe the capabilities of high order discontinuous Galerkin methods at the Institute for Aerodynamics and Gasdynamics for the Large-Eddy Simulation of wall-bounded flows at moderate Reynolds numbers. In these scenarios, the prediction of laminar regions, flow transition and developed turbulence poses a great challenge to the numerical scheme, as overprediction of numerical dissipation can significantly influence the accuracy of the integral quantities. While this increases the burden on the numerical scheme and the LES subgrid model, the moderate Reynolds numbers prevent the occurrence of thin wall boundary layers and allows the resolution of the boundary layer without the need for wall modelling strategies. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high order spectral approximations by using high order ansatz functions up to 12th order, which allows us to resolve the significant features of these flows at a very low number of degrees of freedom. Without the need for any additional filtering, explicit or implicit modelling or artificial dissipation, the high order scheme capture the turbulent flow at the considered Reynolds number range very well.

Advances in the Computational Aeroacoustics with the Discontinuous Galerkin Solver NoisSol

In this work modifications for the aeroacoustic solver NoisSol are presented. This code applies the high order ADER-Discontinuous Galerkin scheme for the solution of linearized acoustic equations in inhomogeneous mean flow conditions. At first the current state of the scheme is presented and the problems, that can arise under certain mean flow conditions are discussed. Then dierent approaches are shown to solve those problems. These include variable Jacobi matrices, a new time integration method called Taylor-DG and a modified surface integration method based on a nodal data basis. In the last part some results are shown. These include a simple convergence test to show the operability of the modified schemes in comparison to the established one and a Single Cylinder Scattering test case with an inhomogeneous background flow to show the potential of the new schemes.

High Order and Underresolution

In this work, the accuracy of high order discontinuous Galerkin discretizations for underresolved problems is investigated. Whereas the superior behavior of high order methods for the well resolved case is undisputed, in case of underresolution, the answer is not as clear. The controversy originates from the fact that order of convergence is a concept for discretization parameters tending to zero, whereas underresolution is synonym for large discretization parameters. However, this work shows that even in the case of underresolution, high order discontinuous Galerkin approximations yield superior efficiency compared to their lower order variants due to the better dispersion and dissipation behavior. It is furthermore shown that a very high order accurate discretization (theoretically 16th order in this case) yields even better accuracy than state-of-the-art large eddy simulation methods for the same number of degrees of freedom for the considered example. This result is particularly surprising since those large eddy simulation methods are tuned specifically to capture coarsely resolved turbulence, whereas the considered high order method can be applied directly to a wide range of other multi-scale problems without additional parameter tuning.

Application and Development of the High Order Discontinuous Galerkin Spectral Element Method for Compressible Multiscale Flows

This paper summarizes our progress in the application of a high-order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations on the Cray XC40 Hazel Hen cluster at HLRS. We present the large eddy simulation (LES) of flow around a wall mounted cylinder, a LES of flow around an airfoil at realistic Reynolds number using a recently introduced kinetic energy preserving flux formulation and a simulation of transitional flow in a low pressure turbine. Furthermore, it provides an overview over the parallel efficiency reached by our code when using up to 49, 152 CPUs and the latest developments of our DG framework.

High Fidelity Scale-Resolving Computational Fluid Dynamics Using the High Order Discontinuous Galerkin Spectral Element Method

In this report we give an overview of our high-order simulations of turbulent flows carried out on the HLRS systems. The simulation framework is built around a highly scalable solver based on the discontinuous Galerkin spectral element method (DGSEM). It has been designed to support large scale simulations on massively parallel architectures and at the same time enabling the use of complex geometries with unstructured, nonconforming meshes. We are thus capable of fully exploiting the performance of HLRS Cray XE6 (Hermit) and XC40 (Hornet) systems not just for academic benchmark problems but also industrial applications. We exemplify the capabilities of our framework at three recent simulations, where we have performed direct numerical and large eddy simulations of turbulent compressible flows. The test cases include a high-speed turbulent boundary layer flow utilizing close to 94,000 physical cores, a DNS of a NACA 0012 airfoil at Re = 100, 000 and direct aeroacoustic simulations of a close-to-production car mirror at Re c = 100, 000.

On the Effect of Flux Functions in Discontinuous Galerkin Simulations of Underresolved Turbulence

In this work, the influence of the numerical flux functions in the context of an underresolved Discontinuous Galerkin discretization of turbulent compressible flows is investigated. We find that the impact of the choice of the numerical flux function strongly depends on the polynomial degree N, with a larger influence for lower order approximations. Overall, Discontinuous Galerkin discretizations are too dissipative compared to the reference DNS solution, with a lower error for the Roe flux function compared to the local Lax-Friedrichs flux function. This motivates further investigations into Discontinuous Galerkin-based implicit Large Eddy Simulation, an idea supported by results obtained with a low order approximation combined with a modified Roe flux function.