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.

[1]  Christopher K. W. Tam,et al.  Discrete tones of isolated airfoils , 1974 .

[2]  Gregor Gassner,et al.  A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods , 2011, SIAM J. Sci. Comput..

[3]  Miguel R. Visbal,et al.  Implicit Large Eddy Simulation of Low Reynolds Number Flow Past the SD7003 Airfoil , 2008 .

[4]  Jan S. Hesthaven,et al.  A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence , 2005 .

[5]  O. Marxen,et al.  Steady solutions of the Navier-Stokes equations by selective frequency damping , 2006 .

[6]  M. Carpenter,et al.  Fourth-order 2N-storage Runge-Kutta schemes , 1994 .

[7]  Richard D. Sandberg,et al.  Numerical analysis of tonal airfoil self-noise and acoustic feedback-loops , 2011 .

[8]  Tim Colonius,et al.  MODELING ARTIFICIAL BOUNDARY CONDITIONS FOR COMPRESSIBLE FLOW , 2004 .

[9]  David A. Kopriva,et al.  Implementing Spectral Methods for Partial Differential Equations , 2009 .

[10]  Thomas J. R. Hughes,et al.  Weak imposition of Dirichlet boundary conditions in fluid mechanics , 2007 .

[11]  Rémi Abgrall,et al.  High‐order CFD methods: current status and perspective , 2013 .

[12]  Claus-Dieter Munz,et al.  Discontinuous Galerkin Schemes for the Direct Numerical Simulation of Fluid Flow and Acoustics , 2012 .

[13]  H. Arbey,et al.  Noise generated by airfoil profiles placed in a uniform laminar flow , 1983, Journal of Fluid Mechanics.

[14]  Thomas B. Gatski,et al.  The temporally filtered Navier–Stokes equations: Properties of the residual stress , 2003 .

[15]  Claus-Dieter Munz,et al.  High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations , 2014 .

[16]  David A. Kopriva,et al.  Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers , 2009 .

[17]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[18]  G. Taylor The Spectrum of Turbulence , 1938 .

[19]  A. Beck,et al.  On the accuracy of high-order discretizations for underresolved turbulence simulations , 2013 .

[20]  Richard D. Sandberg,et al.  Nonreflecting Zonal Characteristic Boundary Condition for Direct Numerical Simulation of Aerodynamic Sound , 2006 .

[21]  T. Poinsot Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[22]  Steven A. Orszag,et al.  On the Elimination of Aliasing in Finite-Difference Schemes by Filtering High-Wavenumber Components , 1971 .

[23]  David A. Kopriva,et al.  Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes , 2006, J. Sci. Comput..

[24]  George Em Karniadakis,et al.  De-aliasing on non-uniform grids: algorithms and applications , 2003 .

[25]  E. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[26]  M. Selig Summary of low speed airfoil data , 1995 .

[27]  P. Sagaut,et al.  Numerical investigation of the tone noise mechanism over laminar airfoils , 2007, Journal of Fluid Mechanics.