Journal ArticleDOI
On the accuracy of high-order discretizations for underresolved turbulence simulations
Gregor J. Gassner,Andrea Beck +1 more
Reads0
Chats0
TLDR
It is shown that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing, so proper stabilization is necessary for a successful computation of underresolved turbulence.Abstract:
In this paper, we investigate the accuracy of a high-order discontinuous Galerkin discretization for the coarse resolution simulation of turbulent flow. We show that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing. Thus, for high-order simulations of underresolved turbulence, proper stabilization is necessary for a successful computation. Two different mechanisms are chosen, and their impact on the accuracy of underresolved high-order computations of turbulent flows is investigated. Results of these approximations for the Taylor–Green Vortex problem are compared to direct numerical simulation results from literature. Our findings show that the superior discretization properties of high-order approximations are retained even for these coarsely resolved computations.read more
Citations
More filters
Journal ArticleDOI
On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows
Francesco Bassi,Lorenzo Alessio Botti,Alessandro Colombo,Andrea Crivellini,Antonio Ghidoni,Francesco Carlo Massa +5 more
TL;DR: This paper focuses on recent developments and applications of an implicit high-order DG method for the DNS and ILES of both compressible and incompressible flows, achieved using the same numerical technology in both cases.
Journal ArticleDOI
A kinetic energy preserving nodal discontinuous Galerkin spectral element method
TL;DR: This work derives a suitable interface flux that guarantees kinetic energy preservation in combination with the skew‐symmetric DG formulation and uses the summation‐by‐parts (SBP) property of the Gauss–Lobatto‐based DG operator and shows that the novel formulation is exactly conservative for the mass, momentum, and energy.
Journal ArticleDOI
FLEXI: A high order discontinuous Galerkin framework for hyperbolic–parabolic conservation laws
Nico Krais,Andrea Beck,Thomas Bolemann,Hannes Frank,David Flad,Gregor J. Gassner,Florian Hindenlang,Malte Hoffmann,Thomas Kuhn,Matthias Sonntag,Claus-Dieter Munz +10 more
TL;DR: The FLEXI framework is presented, a HO consistent, open-source simulation tool chain for solving the compressible Navier-Stokes equations in a high performance computing setting.
Proceedings ArticleDOI
A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods
TL;DR: The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods and the isentropic Euler vortex problem is used here to empirically verify this claim.
Journal ArticleDOI
Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties
TL;DR: A number of pseudo-symplectic methods are constructed for application to the incompressible Navier-Stokes equations and compared in terms of accuracy and efficiency by means of numerical simulations.
References
More filters
Journal ArticleDOI
On the identification of a vortex
Jinhee Jeong,Fazle Hussain +1 more
TL;DR: In this article, the authors propose a definition of vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor, which captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers.
Book
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Jan S. Hesthaven,Tim Warburton +1 more
TL;DR: The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.
Journal ArticleDOI
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations
Francesco Bassi,Stefano Rebay +1 more
TL;DR: This paper extends a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier?Stokes equations by treating the viscous terms with a mixed formulation, and finds the method is ideally suited to compute high-order accurate solution of theNavier?
Journal ArticleDOI
Small-scale structure of the Taylor–Green vortex
TL;DR: In this article, the dynamics of inviscid and viscous Taylor-Green (TG) vortex flows are investigated by both direct spectral numerical solution of the Navier-Stokes equations and by power-series analysis in time.
Journal ArticleDOI
Direct numerical simulation of turbulent flow over riblets
TL;DR: In this article, a drag reduction mechanism by riblets with small spacings was proposed to reduce viscous drag by restricting the location of the streamwise vortices above the wetted surface.
Related Papers (5)
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations
Francesco Bassi,Stefano Rebay +1 more
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Jan S. Hesthaven,Tim Warburton +1 more