On the accuracy of high-order discretizations for underresolved turbulence simulations

Altmann, C., Beck, A., Hindenlang, F., Staudenmaier, M., Gassner, G.: An efficient high performance parallelization of a discontinuous galerkin spectral element method (in preparation)

Bassi F., Rebay S.: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations. J. Comput. Phys. 131, 267–279 (1997)

Bassi F., Rebay S., Mariotti G., Pedinotti S., Savini M.: A high-order accurate discontinuous finite element method fir inviscid an viscous turbomachinery flows. In: Decuypere, R., Dibelius, G. (eds) Proceedings of 2nd European Conference on Turbomachinery, Fluid and Thermodynamics, pp. 99–108. Technologisch Instituut, Antwerpen (1997)

Berland J., Bogey C., Marsden O., Bailly C.: High-order, low dispersive and low dissipative explicit schemes for multi-scale and boundary problems. J. Comput. Phys. 224, 637–662 (2007)

Black K.: A conservative spectral element method for the approximation of compressible fluid flow. KYBERNETIKA 35(1), 133–146 (1999)

Black K.: Spectral element approximation of convection-diffusion type problems. Appl. Numer. Math. 33(1–4), 373–379 (2000)

Brachet M.: Direct simulation of three-dimensional turbulence in the taylor–green vortex. Fluid Dyn Res 8(1–4), 1–8 (1991)

Brachet M.E., Meiron D.I., Orszag S.A., Nickel B.G., Morf R.H., Frisch U.: Small-scale structure of the Taylor–Green vortex. J. Fluid Mech. 130, 411–452 (1983). doi: 10.1017/S0022112083001159

Castel N., Cohen G., Durufle M.: Application of discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic. J. Comput. Acoust. 17(2), 175–196 (2009)

Choi H., Moin P., Kim J.: Direct numerical simulation of flow over riblets. J. Fluid Mech. 255, 503–539 (1994)

Deng S.: Numerical simulation of optical coupling and light propagation in coupled optical resonators with size disorder. Appl. Numer. Math. 57(5–7), 475–485 (2007). doi: 10.1016/j.apnum.2006.07.001

Deng S., Cai W., Astratov V.: Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides. Opt. Express 12(26), 6468–6480 (2004)

Fagherazzi S., Furbish D., Rasetarinera P., Hussaini M.Y.: Application of the discontinuous spectral Galerkin method to groundwater flow. Adv. Water Resour. 27, 129–140 (2004)

Fagherazzi S., Rasetarinera P., Hussaini M.Y., Furbish D.J.: Numerical solution of the dam-break problem with a discontinuous Galerkin method. J. Hydraul. Eng. 130(6), 532–539 (2004)

Fauconnier, D.: Development of a dynamic finite difference method for large-eddy simulation. Dissertation, Ghent University, Ghent, Belgium (2008)

Fauconnier, D., Bogey, C., Dick, E., Bailly, C.: Assessment of large-eddy simulation based on relaxation filtering: application to the Taylor–Green vortex. In: Proceedings of the Seventh International Symposium on Turbulence and Shear Flow Phenomena, Ottawa, Canada (2011)

Gassner, G., Kopriva, D.: A comparison of the dispersion and dissipation errors of gauss and Gauss–Lobatto discontinuous galerkin spectral element methods. SIAM J. Sci. Comput. 33, 2560–2579

Giraldo F., Hesthaven J., Warburton T.: Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations. J. Comput. Phys. 181(2), 499–525 (2002)

Giraldo F., Restelli M.: A study of spectral element and discontinuous Galerkin methods for the navier–stokes equations in nonhydrostatic mesoscale atmospheric modeling: equation sets and test cases. J. Compt. Phys 227, 3849–3877 (2008)

Hesthaven J., Warburton T.: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer, New York (2008)

Hickel, S.: Implicit turbulence modeling for large-eddy simulation. Dissertation, Technische Universität München, Munich, Germany (2008)

Hickel S., Adams N.A., Domaradzki J.A.: An adaptive local deconvolution method for implicit les. J. Comput. Phys. 213(1), 413–436 (2006)

Hindenlang, F., Gassner, G.J., Altmann, C., Beck, A., Staudenmaier, M., Munz, C.D.: Explicit discontinuous Galerkin methods for unsteady problems (submitted to computers and fluids)

Jeong J., Hussain F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)

Kirby R.M., Karniadakis G.E.: De-aliasing on non-uniform grids: algorithms and applications. J. Comput. Phys. 191(1), 249–264 (2003)

Kopriva, D.: Metric identities and the discontinuous spectral element method on curvilinear meshes. J. Sci. Comput. 26(3), 301–327 (2006). doi: 10.1007/s10915-005-9070-8

Kopriva D., Gassner G.: On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods. J. Sci. Comput. 44(2), 136–155 (2010)

Kopriva D., Woodruff S., Hussaini M.: Discontinuous spectral element approximation of Maxwell’s equations. In: Cockburn, B., Karniadakis, G., Shu, C.W. (eds) Proceedings of the International Symposium on Discontinuous Galerkin Methods, Springer, New York (2000)

Kopriva D., Woodruff S., Hussaini M.: Computation of electromagnetic scattering with a non-conforming discontinuous spectral element method. Int. J. Numer. Methods Eng 53, 105–122 (2002)

Kopriva D.A.: Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers 1st edn. Springer, Berlin (2009)

Mathew J., Foysi H., Friedrich R.: A new approach to les based on explicit filtering. Int. J. Heat Fluid Flow 27, 594–602 (2006)

Pasquetti R.: High-order les modeling of turbulent incompressible flows. C.R. Acad. Sci. Paris 333, 39–49 (2005)

Rasetarinera P., Hussaini M.: An efficient implicit discontinuous spectral Galerkin method. J. Comput. Phys. 172, 718–738 (2001)

Rasetarinera P., Kopriva D., Hussaini M.: Discontinuous spectral element solution of acoustic radiation from thin airfoils. AIAA J. 39(11), 2070–2075 (2001)

Restelli M., Giraldo F.: A conservative discontinuous Galerkin semi-implicit formulation for the Navier–Stokes equations in nonhydrostatic mesoscale modeling. SIAM J. Sci. Comp. 31(3), 2231–2257 (2009)

Stanescu, D., Farassat, F., Hussaini, M.: Aircraft engine noise scattering—parallel discontinuous Galerkin spectral element method. Paper 2002–0800, AIAA (2002)

Stanescu D., Xu J., Farassat F., Hussaini M.: Computation of engine noise propagation and scattering off an aircraft. Aeroacoustics 1(4), 403–420 (2002)

Tadmor E.: Convergence of spectral methods for nonlinear conservation laws. SIAM J. Numer. Anal. 26, 30–44 (1989)

Vreman B., Geurts B., Kuerten H.: Comparison of numerical schemes in large eddy simulation of the temporal mixing layer. Int. J. Numer. Methods Fluids 22, 297–311 (1996)

Yee H.C., Vinokur M., Djomehri M.J.: Entropy splitting and numerical dissipation. J. Comput. Phys. 162(1), 33–81 (2000)