{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T14:50:09Z","timestamp":1768747809351,"version":"3.49.0"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T00:00:00Z","timestamp":1618790400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T00:00:00Z","timestamp":1618790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100007527","name":"Universit\u00e9 de Rouen","doi-asserted-by":"publisher","award":["Th-2018-23-C"],"award-info":[{"award-number":["Th-2018-23-C"]}],"id":[{"id":"10.13039\/501100007527","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s10915-021-01484-1","type":"journal-article","created":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T17:03:34Z","timestamp":1618851814000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Comparative Study from Spectral Analyses of High-Order Methods with Non-Constant Advection Velocities"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7166-2189","authenticated-orcid":false,"given":"Niccol\u00f2","family":"Tonicello","sequence":"first","affiliation":[]},{"given":"Guido","family":"Lodato","sequence":"additional","affiliation":[]},{"given":"Luc","family":"Vervisch","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,19]]},"reference":[{"key":"1484_CR1","unstructured":"Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E., Mavriplis, D.: CFD vision 2030 study: a path to revolutionary computational aerosciences. Technical Report, NASA Langley Research Center, Hampton, Virginia 23681-2199, NASA Contractor Report 218178 (Mar. 2014)"},{"issue":"3","key":"1484_CR2","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1051\/mmnp\/20116305","volume":"6","author":"PE Vincent","year":"2011","unstructured":"Vincent, P.E., Jameson, A.: Facilitating the adoption of unstructured high-order methods amongst a wider community of fluid dynamicists. Math. Model. Nat. Phenomena 6(3), 97\u2013140 (2011)","journal-title":"Math. Model. Nat. Phenomena"},{"key":"1484_CR3","unstructured":"Fernandez, P., Nguyen, N.-C., Peraire, J.: On the ability of discontinuous Galerkin methods to simulate under-resolved turbulent flows. Preprint arXiv:1810.09435"},{"key":"1484_CR4","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1016\/j.jcp.2017.02.015","volume":"336","author":"P Fernandez","year":"2017","unstructured":"Fernandez, P., Nguyen, N., Peraire, J.: The hybridized discontinuous Galerkin method for implicit large-eddy simulation of transitional turbulent flows. J. Comput. Phys. 336, 308\u2013329 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2017.02.015","journal-title":"J. Comput. Phys."},{"key":"1484_CR5","unstructured":"Fernandez, P., Nguyen, N.-C., Peraire, J.: Entropy-stable hybridized discontinuous Galerkin methods for the compressible Euler and Navier\u2013Stokes equations. Preprint arXiv:1808.05066"},{"issue":"8","key":"1484_CR6","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1002\/fld.3943","volume":"76","author":"AD Beck","year":"2014","unstructured":"Beck, A.D., Bolemann, T., Flad, D., Frank, H., Gassner, G.J., Hindenlang, F., Munz, C.-D.: High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. Int. J. Numer. Methods Fluids 76(8), 522\u2013548 (2014). https:\/\/doi.org\/10.1002\/fld.3943","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"1484_CR7","doi-asserted-by":"publisher","first-page":"782","DOI":"10.1016\/j.jcp.2017.09.004","volume":"350","author":"D Flad","year":"2017","unstructured":"Flad, D., Gassner, G.: On the use of kinetic energy preserving dg-schemes for large eddy simulation. J. Comput. Phys. 350, 782\u2013795 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2017.09.004","journal-title":"J. Comput. Phys."},{"key":"1484_CR8","volume-title":"Spectral\/HP Element Methods for Computational Fluid Dynamics","author":"G Karniadakis","year":"2013","unstructured":"Karniadakis, G., Sherwin, S.: Spectral\/HP Element Methods for Computational Fluid Dynamics. Oxford University Press, Oxford (2013)"},{"issue":"1","key":"1484_CR9","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/0021-9991(92)90324-R","volume":"103","author":"SK Lele","year":"1992","unstructured":"Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103(1), 16\u201342 (1992)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1484_CR10","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.jcp.2003.09.003","volume":"194","author":"C Bogey","year":"2004","unstructured":"Bogey, C., Bailly, C.: A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194(1), 194\u2013214 (2004)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1484_CR11","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/s10915-008-9201-0","volume":"37","author":"K Van den Abeele","year":"2008","unstructured":"Van den Abeele, K., Lacor, C., Wang, Z.J.: On the stability and accuracy of the spectral difference method. J. Sci. Comput. 37(2), 162\u2013188 (2008)","journal-title":"J. Sci. Comput."},{"issue":"22","key":"1484_CR12","doi-asserted-by":"publisher","first-page":"8134","DOI":"10.1016\/j.jcp.2011.07.013","volume":"230","author":"PE Vincent","year":"2011","unstructured":"Vincent, P.E., Castonguay, P., Jameson, A.: Insights from von Neumann analysis of high-order flux reconstruction schemes. J. Comput. Phys. 230(22), 8134\u20138154 (2011)","journal-title":"J. Comput. Phys."},{"key":"1484_CR13","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1016\/j.jcp.2015.06.020","volume":"298","author":"RC Moura","year":"2015","unstructured":"Moura, R.C., Sherwin, S.J., Peir\u00f3, J.: Linear dispersion\u2013diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral\/HP methods. J. Comput. Phys. 298, 695\u2013710 (2015)","journal-title":"J. Comput. Phys."},{"key":"1484_CR14","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/j.jcp.2017.02.043","volume":"337","author":"J Vanharen","year":"2017","unstructured":"Vanharen, J., Puigt, G., Vasseur, X., Boussuge, J.-F., Sagaut, P.: Revisiting the spectral analysis for high-order spectral discontinuous methods. J. Comput. Phys. 337, 379\u2013402 (2017)","journal-title":"J. Comput. Phys."},{"key":"1484_CR15","volume-title":"Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications","author":"JS Hesthaven","year":"2007","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer, Berlin (2007)"},{"key":"1484_CR16","doi-asserted-by":"publisher","first-page":"2440","DOI":"10.1137\/S0036142997316712","volume":"35","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.: The local discontinuous Galerkin finite element method for convection\u2013diffusion systems. SIAM J. Numer. Anal. 35, 2440\u20132463 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"1484_CR17","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jcph.1998.5892","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.: The Runge\u2013Kutta discontinuous Galerkin finite element method for conservation laws V: multidimensional systems. J. Comput. Phys. 141, 199\u2013224 (1998)","journal-title":"J. Comput. Phys."},{"key":"1484_CR18","doi-asserted-by":"crossref","unstructured":"Huynh, H.T.: A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. In: 18th AIAA Computational Fluid Dynamics Conference, p. 4079 (2007)","DOI":"10.2514\/6.2007-4079"},{"issue":"1","key":"1484_CR19","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s10915-010-9420-z","volume":"47","author":"PE Vincent","year":"2011","unstructured":"Vincent, P.E., Castonguay, P., Jameson, A.: A new class of high-order energy stable flux reconstruction schemes. J. Sci. Comput. 47(1), 50\u201372 (2011)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"1484_CR20","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1006\/jcph.1996.0091","volume":"125","author":"DA Kopriva","year":"1996","unstructured":"Kopriva, D.A., Kolias, J.H.: A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys. 125(1), 244\u2013261 (1996)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1484_CR21","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1016\/j.jcp.2006.01.024","volume":"216","author":"Y Liu","year":"2006","unstructured":"Liu, Y., Vinokur, M., Wang, Z.: Spectral difference method for unstructured grids I: basic formulation. J. Comput. Phys. 216(2), 780\u2013801 (2006)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1484_CR22","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10915-006-9113-9","volume":"32","author":"Z Wang","year":"2007","unstructured":"Wang, Z., Liu, Y., May, G., Jameson, A.: Spectral difference method for unstructured grids II: extension to the Euler equations. J. Sci. Comput. 32(1), 45\u201371 (2007)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1484_CR23","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1006\/jcph.2002.7184","volume":"182","author":"FQ Hu","year":"2002","unstructured":"Hu, F.Q., Atkins, H.L.: Eigensolution analysis of the discontinuous Galerkin method with nonuniform grids: I. One space dimension. J. Comput. Phys. 182(2), 516\u2013545 (2002)","journal-title":"J. Comput. Phys."},{"key":"1484_CR24","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/j.compfluid.2017.09.016","volume":"169","author":"G Mengaldo","year":"2018","unstructured":"Mengaldo, G., Moura, R., Giralda, B., Peir\u00f3, J., Sherwin, S.: Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES. Comput. Fluids 169, 349\u2013364 (2018)","journal-title":"Comput. Fluids"},{"key":"1484_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jcp.2017.12.019","volume":"358","author":"G Mengaldo","year":"2018","unstructured":"Mengaldo, G., De Grazia, D., Moura, R.C., Sherwin, S.J.: Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness. J. Comput. Phys. 358, 1\u201320 (2018)","journal-title":"J. Comput. Phys."},{"key":"1484_CR26","doi-asserted-by":"publisher","first-page":"109112","DOI":"10.1016\/j.jcp.2019.109112","volume":"406","author":"R Moura","year":"2019","unstructured":"Moura, R., Aman, M., Peir\u00f3, J., Sherwin, S.: Spatial eigenanalysis of spectral\/HP continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity: application to high Reynolds number flows. J. Comput. Phys. 406, 109112 (2019)","journal-title":"J. Comput. Phys."},{"key":"1484_CR27","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1146\/annurev.fluid.38.050304.092139","volume":"39","author":"PJ Schmid","year":"2007","unstructured":"Schmid, P.J.: Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129\u2013162 (2007)","journal-title":"Annu. Rev. Fluid Mech."},{"issue":"5121","key":"1484_CR28","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1126\/science.261.5121.578","volume":"261","author":"LN Trefethen","year":"1993","unstructured":"Trefethen, L.N., Trefethen, A.E., Reddy, S.C., Driscoll, T.A.: Hydrodynamic stability without eigenvalues. Science 261(5121), 578\u2013584 (1993)","journal-title":"Science"},{"issue":"3","key":"1484_CR29","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1137\/S0036144595295284","volume":"39","author":"LN Trefethen","year":"1997","unstructured":"Trefethen, L.N.: Pseudospectra of linear operators. SIAM Rev. 39(3), 383\u2013406 (1997)","journal-title":"SIAM Rev."},{"issue":"2","key":"1484_CR30","doi-asserted-by":"publisher","first-page":"A747","DOI":"10.1137\/16M1101143","volume":"40","author":"J Manzanero","year":"2018","unstructured":"Manzanero, J., Rubio, G., Ferrer, E., Valero, E.: Dispersion-dissipation analysis for advection problems with nonconstant coefficients: applications to discontinuous Galerkin formulations. SIAM J. Sci. Comput. 40(2), A747\u2013A768 (2018)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1484_CR31","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1007\/s10915-017-0585-6","volume":"75","author":"J Manzanero","year":"2017","unstructured":"Manzanero, J., Rubio, G., Ferrer, E., Valero, E., Kopriva, D.A.: Insights on aliasing driven instabilities for advection equations with application to Gauss\u2013Lobatto discontinuous Galerkin methods. J. Sci. Comput. 75(3), 1262\u20131281 (2017)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"1484_CR32","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1007\/s10915-009-9339-4","volume":"45","author":"A Jameson","year":"2010","unstructured":"Jameson, A.: A proof of the stability of the spectral difference method for all orders of accuracy. J. Sci. Comput. 45(1), 348\u2013358 (2010)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1484_CR33","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1007\/s10915-011-9490-6","volume":"50","author":"A Jameson","year":"2012","unstructured":"Jameson, A., Vincent, P., Castonguay, P.: On the non-linear stability of flux reconstruction schemes. J. Sci. Comput. 50(2), 434\u2013445 (2012)","journal-title":"J. Sci. Comput."},{"key":"1484_CR34","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.cma.2018.11.027","volume":"346","author":"P Fernandez","year":"2019","unstructured":"Fernandez, P., Moura, R.C., Mengaldo, G., Peraire, J.: Non-modal analysis of spectral element methods: towards accurate and robust large-eddy simulations. Comput. Methods Appl. Mech. Eng. 346, 43\u201362 (2019). https:\/\/doi.org\/10.1016\/j.cma.2018.11.027","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"1484_CR35","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1007\/s10915-014-9882-5","volume":"62","author":"K Asthana","year":"2015","unstructured":"Asthana, K., Jameson, A.: High-order flux reconstruction schemes with minimal dispersion and dissipation. J. Sci. Comput. 62(3), 913\u2013944 (2015)","journal-title":"J. Sci. Comput."},{"issue":"11\u201312","key":"1484_CR36","doi-asserted-by":"publisher","first-page":"812","DOI":"10.1016\/j.compstruc.2008.12.016","volume":"87","author":"C Liang","year":"2009","unstructured":"Liang, C., Premasuthan, S., Jameson, A.: High-order accurate simulation of low-Mach laminar flow past two side-by-side cylinders using spectral difference method. Comput. Struct. 87(11\u201312), 812\u2013827 (2009)","journal-title":"Comput. Struct."},{"issue":"8","key":"1484_CR37","doi-asserted-by":"publisher","first-page":"2847","DOI":"10.1016\/j.jcp.2008.12.038","volume":"228","author":"C Liang","year":"2009","unstructured":"Liang, C., Jameson, A., Wang, Z.J.: Spectral difference method for compressible flow on unstructured grids with mixed elements. J. Comput. Phys. 228(8), 2847\u20132858 (2009)","journal-title":"J. Comput. Phys."},{"key":"1484_CR38","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/j.cpc.2015.02.008","volume":"192","author":"C Cantwell","year":"2015","unstructured":"Cantwell, C., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., Grazia, D.D., Yakovlev, S., Lombard, J.-E., Ekelschot, D., Jordi, B., Xu, H., Mohamied, Y., Eskilsson, C., Nelson, B., Vos, P., Biotto, C., Kirby, R., Sherwin, S.: Nektar++: an open-source spectral\/HP element framework. Comput. Phys. Commun. 192, 205\u2013219 (2015). https:\/\/doi.org\/10.1016\/j.cpc.2015.02.008","journal-title":"Comput. Phys. Commun."},{"issue":"895","key":"1484_CR39","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1098\/rspa.1937.0036","volume":"158","author":"GI Taylor","year":"1937","unstructured":"Taylor, G.I., Green, A.E.: Mechanism of the production of small eddies from large ones. Proc. R. Soc. Lond. A 158(895), 499\u2013521 (1937)","journal-title":"Proc. R. Soc. Lond. A"},{"key":"1484_CR40","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.compfluid.2016.03.006","volume":"139","author":"J-B Chapelier","year":"2016","unstructured":"Chapelier, J.-B., Lodato, G., Jameson, A.: A study on the numerical dissipation of the spectral difference method for freely decaying and wall-bounded turbulence. Comput. Fluids 139, 261\u2013280 (2016). https:\/\/doi.org\/10.1016\/j.compfluid.2016.03.006","journal-title":"Comput. Fluids"},{"key":"1484_CR41","unstructured":"Manzanero, J., Ferrer, E., Rubio, G., Valero, E.: On the role of numerical dissipation in stabilising under-resolved turbulent simulations using discontinuous Galerkin methods (2018)"},{"key":"1484_CR42","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1016\/j.jcp.2016.10.056","volume":"330","author":"RC Moura","year":"2017","unstructured":"Moura, R.C., Mengaldo, G., Peir\u00f3, J., Sherwin, S.J.: On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES\/under-resolved DNS of Euler turbulence. J. Comput. Phys. 330, 615\u2013623 (2017)","journal-title":"J. Comput. Phys."},{"key":"1484_CR43","doi-asserted-by":"publisher","unstructured":"Chapelier, J.-B., Lodato, G.: Optimal high-order Spectral Difference schemes for the computation of aeroacoustics and turbulence. AIAA Paper 2017-1228 (2017) 1\u201317, 55th AIAA Aerospace Sciences Meeting, Grapevine, TX, Jan.\u00a09\u201313 (2017). https:\/\/doi.org\/10.2514\/6.2017-1228","DOI":"10.2514\/6.2017-1228"},{"issue":"2","key":"1484_CR44","doi-asserted-by":"publisher","first-page":"921","DOI":"10.1006\/jcph.1999.6227","volume":"151","author":"FQ Hu","year":"1999","unstructured":"Hu, F.Q., Hussaini, M., Rasetarinera, P.: An analysis of the discontinuous Galerkin method for wave propagation problems. J. Comput. Phys. 151(2), 921\u2013946 (1999)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01484-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01484-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01484-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T18:26:05Z","timestamp":1621880765000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01484-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,19]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1484"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01484-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,19]]},"assertion":[{"value":"23 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 December 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"65"}}