{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T05:10:14Z","timestamp":1747804214893,"version":"3.37.3"},"reference-count":82,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T00:00:00Z","timestamp":1691366400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T00:00:00Z","timestamp":1691366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["RTI2018-096064-B-C21","RTI2018-096064-B-C22"],"award-info":[{"award-number":["RTI2018-096064-B-C21","RTI2018-096064-B-C22"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-114688RB-I00"],"award-info":[{"award-number":["PID2020-114688RB-I00"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["ERC-CG-2013-PE10-617472"],"award-info":[{"award-number":["ERC-CG-2013-PE10-617472"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Digital Twin project","award":["DT-GEO"],"award-info":[{"award-number":["DT-GEO"]}]},{"name":"EnvSeis Doctoral Network","award":["EnvSeis Doctoral Network"],"award-info":[{"award-number":["EnvSeis Doctoral Network"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1007\/s10915-023-02299-y","type":"journal-article","created":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T11:02:55Z","timestamp":1691406175000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multilayer Shallow Model for Dry Granular Flows with a Weakly Non-hydrostatic Pressure"],"prefix":"10.1007","volume":"96","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7602-5920","authenticated-orcid":false,"given":"C.","family":"Escalante","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. D.","family":"Fern\u00e1ndez-Nieto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2013-6127","authenticated-orcid":false,"given":"J.","family":"Garres-D\u00edaz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Mangeney","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"key":"2299_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139541008","volume-title":"Granular Media: Between Fluid and Solid","author":"B Andreotti","year":"2013","unstructured":"Andreotti, B., Forterre, Y., Pouliquen, O.: Granular Media: Between Fluid and Solid. Cambridge University Press, Cambridge (2013). https:\/\/doi.org\/10.1017\/CBO9781139541008"},{"key":"2299_CR2","doi-asserted-by":"publisher","unstructured":"Audusse, E., Bristeau, M., Perthame, B., Sainte-Marie, J.: A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. ESAIM: Math. Modell. Numer. Anal. 45(1), 169\u2013200 (2010). https:\/\/doi.org\/10.1051\/m2an\/2010036","DOI":"10.1051\/m2an\/2010036"},{"issue":"3","key":"2299_CR3","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1002\/fld.1534","volume":"56","author":"E Audusse","year":"2008","unstructured":"Audusse, E., Bristeau, M.O., Decoene, A.: Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model. Int. J. Numer. Meth. Fluids 56(3), 331\u2013350 (2008)","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"2299_CR4","doi-asserted-by":"publisher","first-page":"187","DOI":"10.5802\/smai-jcm.66","volume":"6","author":"N A\u00efssiouene","year":"2020","unstructured":"A\u00efssiouene, N., Bristeau, M.O., Godlewski, E., Mangeney, A., Par\u00e9s Madro\u00f1al, C., Sainte-Marie, J.: A two-dimensional method for a family of dispersive shallow water models. SMAI J. Comput. Math. 6, 187\u2013226 (2020). https:\/\/doi.org\/10.5802\/smai-jcm.66","journal-title":"SMAI J. Comput. Math."},{"key":"2299_CR5","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1017\/jfm.2017.428","volume":"828","author":"T Barker","year":"2017","unstructured":"Barker, T., Gray, J.M.N.T.: Partial regularisation of the incompressible $$\\mu $$(I)-rheology for granular flow. J. Fluid Mech. 828, 5\u201332 (2017). https:\/\/doi.org\/10.1017\/jfm.2017.428","journal-title":"J. Fluid Mech."},{"key":"2299_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2020.973","author":"T Barker","year":"2020","unstructured":"Barker, T., Rauter, M., Maguire, E.S.F., Johnson, C.G., Gray, J.M.N.T.: Coupling rheology and segregation in granular flows. J. Fluid Mech. (2020). https:\/\/doi.org\/10.1017\/jfm.2020.973","journal-title":"J. Fluid Mech."},{"key":"2299_CR7","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1017\/jfm.2015.412","volume":"779","author":"T Barker","year":"2015","unstructured":"Barker, T., Schaeffer, D.G., Bohorquez, P., Gray, J.M.N.T.: Well-posed and ill-posed behaviour of the $$\\mu $$(I)-rheology for granular flow. J. Fluid Mech. 779, 794\u2013818 (2015). https:\/\/doi.org\/10.1017\/jfm.2015.412","journal-title":"J. Fluid Mech."},{"issue":"2201","key":"2299_CR8","doi-asserted-by":"publisher","first-page":"20160846","DOI":"10.1098\/rspa.2016.0846","volume":"473","author":"T Barker","year":"2017","unstructured":"Barker, T., Schaeffer, D.G., Shearer, M., Gray, J.M.N.T.: Well-posed continuum equations for granular flow with compressibility and $$\\mu $$(I)-rheology. Proc. R. Soc. A: Math. Phys. Eng. Sci. 473(2201), 20160846 (2017). https:\/\/doi.org\/10.1098\/rspa.2016.0846","journal-title":"Proc. R. Soc. A: Math. Phys. Eng. Sci."},{"key":"2299_CR9","doi-asserted-by":"crossref","unstructured":"Bouchut, F.: Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws. Birkh\u00e4user Basel (2004). https:\/\/www.ebook.de\/de\/product\/2846251\/francois_bouchut_nonlinear_stability_of_finite_volume_methods_for_hyperbolic_conservation_laws.html","DOI":"10.1007\/b93802"},{"key":"2299_CR10","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.apm.2022.01.034","volume":"106","author":"F Bouchut","year":"2022","unstructured":"Bouchut, F., Delgado-S\u00e1nchez, J.M., Fern\u00e1ndez-Nieto, E.D., Mangeney, A., Narbona-Reina, G.: A bed pressure correction of the friction term for depth-averaged granular flow models. Appl. Math. Model. 106, 627\u2013658 (2022). https:\/\/doi.org\/10.1016\/j.apm.2022.01.034","journal-title":"Appl. Math. Model."},{"key":"2299_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.110013","volume":"429","author":"F Bouchut","year":"2021","unstructured":"Bouchut, F., Fern\u00e1ndez-Nieto, E.D., Kon\u00e9, E.H., Mangeney, A., Narbona-Reina, G.: Dilatancy in dry granular flows with a compressible $$\\mu $$(i) rheology. J. Comput. Phys. 429, 110013 (2021). https:\/\/doi.org\/10.1016\/j.jcp.2020.110013","journal-title":"J. Comput. Phys."},{"key":"2299_CR12","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1017\/jfm.2016.417","volume":"801","author":"F Bouchut","year":"2016","unstructured":"Bouchut, F., Fern\u00e1ndez-Nieto, E.D., Mangeney, A., Narbona-Reina, G.: A two-phase two-layer model for fluidized granular flows with dilatancy effects. J. Fluid Mech. 801, 166\u2013221 (2016). https:\/\/doi.org\/10.1017\/jfm.2016.417","journal-title":"J. Fluid Mech."},{"issue":"8","key":"2299_CR13","doi-asserted-by":"publisher","first-page":"2101","DOI":"10.4310\/cms.2016.v14.n8.a2","volume":"14","author":"F Bouchut","year":"2016","unstructured":"Bouchut, F., Ionescu, I., Mangeney, A.: An analytic approach for the evolution of the static\/flowing interface in viscoplastic granular flows. Commun. Math. Sci. 14(8), 2101\u20132126 (2016). https:\/\/doi.org\/10.4310\/cms.2016.v14.n8.a2","journal-title":"Commun. Math. Sci."},{"key":"2299_CR14","doi-asserted-by":"crossref","unstructured":"Bouchut, F., Westdickenberg, M.: Gravity driven shallow water models for arbitrary topography. Commun. Math. Sci. 2(3), 359\u2013389 (2004)","DOI":"10.4310\/CMS.2004.v2.n3.a2"},{"key":"2299_CR15","unstructured":"Boussinesq, J.: Th\u00e9orie des ondes et des remous qui se propagent le long d\u2019un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. J. Math. Pures Appl. 55\u2013108 (1872)"},{"key":"2299_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.111.238301","author":"M Bouzid","year":"2013","unstructured":"Bouzid, M., Trulsson, M., Claudin, P., Cl\u00e9ment, E., Andreotti, B.: Nonlocal rheology of granular flows across yield conditions. Phys. Rev. Lett. (2013). https:\/\/doi.org\/10.1103\/physrevlett.111.238301","journal-title":"Phys. Rev. Lett."},{"key":"2299_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.107.188301","author":"F Boyer","year":"2011","unstructured":"Boyer, F., Guazzelli, \u00c9., Pouliquen, O.: Unifying suspension and granular rheology. Phys. Rev. Lett. (2011). https:\/\/doi.org\/10.1103\/physrevlett.107.188301","journal-title":"Phys. Rev. Lett."},{"issue":"5","key":"2299_CR18","doi-asserted-by":"publisher","first-page":"1221","DOI":"10.4310\/cms.2017.v15.n5.a3","volume":"15","author":"MO Bristeau","year":"2017","unstructured":"Bristeau, M.O., Guichard, C., di Martino, B., Sainte-Marie, J.: Layer-averaged Euler and Navier\u2013Stokes equations. Commun. Math. Sci. 15(5), 1221\u20131246 (2017). https:\/\/doi.org\/10.4310\/cms.2017.v15.n5.a3","journal-title":"Commun. Math. Sci."},{"issue":"2","key":"2299_CR19","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1007\/s11069-017-2815-5","volume":"87","author":"M Brunet","year":"2017","unstructured":"Brunet, M., Moretti, L., Le Friant, A., Mangeney, A., Fern\u00e1ndez Nieto, E.D., Bouchut, F.: Numerical simulation of the 30\u201345 ka debris avalanche flow of Montagne Pel\u00e9e volcano, Martinique: from volcano flank collapse to submarine emplacement. Nat. Hazards 87(2), 1189\u20131222 (2017). https:\/\/doi.org\/10.1007\/s11069-017-2815-5","journal-title":"Nat. Hazards"},{"key":"2299_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-021-01429-8","author":"S Busto","year":"2021","unstructured":"Busto, S., Dumbser, M., Escalante, C., Favrie, N., Gavrilyuk, S.: On high order ADER Discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems. J. Sci. Comput. (2021). https:\/\/doi.org\/10.1007\/s10915-021-01429-8","journal-title":"J. Sci. Comput."},{"issue":"06","key":"2299_CR21","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1142\/s021820250600139x","volume":"16","author":"MJ Castro","year":"2006","unstructured":"Castro, M.J., Gonz\u00e1lez-Vida, J.M., Par\u00e9s, C.: Numerical treatment of wet\/dry fronts in shallow flows with a modified Roe scheme. Math. Models Methods Appl. Sci. 16(06), 897\u2013931 (2006). https:\/\/doi.org\/10.1142\/s021820250600139x","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"4","key":"2299_CR22","doi-asserted-by":"publisher","first-page":"A2173","DOI":"10.1137\/100795280","volume":"34","author":"MJ Castro D\u00edaz","year":"2012","unstructured":"Castro D\u00edaz, M.J., Fern\u00e1ndez-Nieto, E.D.: A class of computationally fast first order finite volume solvers: PVM methods. SIAM J. Sci. Comput. 34(4), A2173\u2013A2196 (2012). https:\/\/doi.org\/10.1137\/100795280","journal-title":"SIAM J. Sci. Comput."},{"key":"2299_CR23","doi-asserted-by":"crossref","unstructured":"Casulli, V.: A semi-implicit finite difference method for non-hydrostatic free-surface flows. Int. J. Numer. Methods Fluids 30(4), 425\u2013440 (1999). https:\/\/doi.org\/10.1002\/(sici)1097-0363(19990630)30:4<425::aid-fld847>3.0.co;2-d","DOI":"10.1002\/(SICI)1097-0363(19990630)30:4<425::AID-FLD847>3.0.CO;2-D"},{"issue":"9\u201310","key":"2299_CR24","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1016\/s0895-7177(02)00264-9","volume":"36","author":"V Casulli","year":"2002","unstructured":"Casulli, V., Zanolli, P.: Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems. Math. Comput. Model. 36(9\u201310), 1131\u20131149 (2002). https:\/\/doi.org\/10.1016\/s0895-7177(02)00264-9","journal-title":"Math. Comput. Model."},{"key":"2299_CR25","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1016\/j.jcp.2013.09.004","volume":"256","author":"J Chauchat","year":"2014","unstructured":"Chauchat, J., M\u00e9dale, M.: A three-dimensional numerical model for dense granular flows based on the $$\\mu $$(I)-rheology. J. Comput. Phys. 256, 696\u2013712 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2013.09.004","journal-title":"J. Comput. Phys."},{"issue":"104","key":"2299_CR26","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1090\/s0025-5718-1968-0242392-2","volume":"22","author":"AJ Chorin","year":"1968","unstructured":"Chorin, A.J.: Numerical solution of the Navier\u2013Stokes equations. Math. Comput. 22(104), 745\u2013762 (1968). https:\/\/doi.org\/10.1090\/s0025-5718-1968-0242392-2","journal-title":"Math. Comput."},{"issue":"2","key":"2299_CR27","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1006\/jcph.2001.6961","volume":"175","author":"A Dedner","year":"2002","unstructured":"Dedner, A., Kemm, F., Kr\u00f6ner, D., Munz, C.D., Schnitzer, T., Wesenberg, M.: Hyperbolic divergence cleaning for the MHD equations. J. Comput. Phys. 175(2), 645\u2013673 (2002). https:\/\/doi.org\/10.1006\/jcph.2001.6961","journal-title":"J. Comput. Phys."},{"issue":"5","key":"2299_CR28","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/50\/5\/053001","volume":"50","author":"R Delannay","year":"2017","unstructured":"Delannay, R., Valance, A., Mangeney, A., Roche, O., Richard, P.: Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D: Appl. Phys. 50(5), 053001 (2017)","journal-title":"J. Phys. D: Appl. Phys."},{"key":"2299_CR29","doi-asserted-by":"publisher","unstructured":"Denlinger, R.P., Iverson, R.M.: Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation. J. Geophys. Res.: Earth Surface (2004). https:\/\/doi.org\/10.1029\/2003jf000085","DOI":"10.1029\/2003jf000085"},{"key":"2299_CR30","doi-asserted-by":"publisher","unstructured":"Escalante, C., Fern\u00e1ndez-Nieto, E.D., Morales de Luna, T., Castro, M.J.: An efficient two-layer non-hydrostatic approach for dispersive water waves. J. Sci. Comput. 79(1), 273\u2013320 (2018). https:\/\/doi.org\/10.1007\/s10915-018-0849-9","DOI":"10.1007\/s10915-018-0849-9"},{"issue":"338","key":"2299_CR31","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1016\/j.amc.2018.06.035","volume":"338","author":"C Escalante","year":"2018","unstructured":"Escalante, C., de Luna, T.M., Castro, M.J.: Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme. Appl. Math. Comput. 338(338), 631\u2013659 (2018). https:\/\/doi.org\/10.1016\/j.amc.2018.06.035","journal-title":"Appl. Math. Comput."},{"key":"2299_CR32","doi-asserted-by":"publisher","unstructured":"Escalante, C., Morales de Luna, T.: A general non-hydrostatic hyperbolic formulation for Boussinesq dispersive shallow flows and its numerical approximation. J. Sci. Comput. (2020). https:\/\/doi.org\/10.1007\/s10915-020-01244-7","DOI":"10.1007\/s10915-020-01244-7"},{"key":"2299_CR33","doi-asserted-by":"publisher","unstructured":"Escalante S\u00e1nchez, C., Fern\u00e1ndez-Nieto, E.D., Morales de Luna, T., Penel, Y., Sainte-Marie, J.: Numerical simulations of a dispersive model approximating free-surface Euler equations. J. Sci. Comput. 89(3) (2021). https:\/\/doi.org\/10.1007\/s10915-021-01552-6","DOI":"10.1007\/s10915-021-01552-6"},{"issue":"7","key":"2299_CR34","doi-asserted-by":"publisher","first-page":"2718","DOI":"10.1088\/1361-6544\/aa712d","volume":"30","author":"N Favrie","year":"2017","unstructured":"Favrie, N., Gavrilyuk, S.: A rapid numerical method for solving Serre\u2013Green\u2013Naghdi equations describing long free surface gravity waves. Nonlinearity 30(7), 2718\u20132736 (2017). https:\/\/doi.org\/10.1088\/1361-6544\/aa712d","journal-title":"Nonlinearity"},{"issue":"16","key":"2299_CR35","doi-asserted-by":"publisher","first-page":"7720","DOI":"10.1016\/j.jcp.2008.04.039","volume":"227","author":"ED Fern\u00e1ndez-Nieto","year":"2008","unstructured":"Fern\u00e1ndez-Nieto, E.D., Bouchut, F., Bresch, D., Castro D\u00edaz, M.J., Mangeney, A.: A new Savage\u2013Hutter type model for submarine avalanches and generated tsunami. J. Comput. Phys. 227(16), 7720\u20137754 (2008). https:\/\/doi.org\/10.1016\/j.jcp.2008.04.039","journal-title":"J. Comput. Phys."},{"key":"2299_CR36","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1017\/jfm.2016.333","volume":"798","author":"ED Fern\u00e1ndez-Nieto","year":"2016","unstructured":"Fern\u00e1ndez-Nieto, E.D., Garres-D\u00edaz, J., Mangeney, A., Narbona-Reina, G.: A multilayer shallow model for dry granular flows with the $$\\mu ({I})$$-rheology: application to granular collapse on erodible beds. J. Fluid Mech. 798, 643\u2013681 (2016). https:\/\/doi.org\/10.1017\/jfm.2016.333","journal-title":"J. Fluid Mech."},{"key":"2299_CR37","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1016\/j.jcp.2017.11.038","volume":"356","author":"ED Fern\u00e1ndez-Nieto","year":"2018","unstructured":"Fern\u00e1ndez-Nieto, E.D., Garres-D\u00edaz, J., Mangeney, A., Narbona-Reina, G.: 2D granular flows with the $$\\mu ({I})$$ rheology and side walls friction: a well-balanced multilayer discretization. J. Comput. Phys. 356, 192\u2013219 (2018). https:\/\/doi.org\/10.1016\/j.jcp.2017.11.038","journal-title":"J. Comput. Phys."},{"key":"2299_CR38","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.camwa.2023.03.018","volume":"139","author":"ED Fern\u00e1ndez-Nieto","year":"2023","unstructured":"Fern\u00e1ndez-Nieto, E.D., Garres-D\u00edaz, J., Vigneaux, P.: Multilayer models for hydrostatic Herschel\u2013Bulkley viscoplastic flows. Comput. Math. Appl. 139, 99\u2013117 (2023). https:\/\/doi.org\/10.1016\/j.camwa.2023.03.018","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"2299_CR39","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1007\/s10915-013-9802-0","volume":"60","author":"ED Fern\u00e1ndez-Nieto","year":"2013","unstructured":"Fern\u00e1ndez-Nieto, E.D., Kon\u00e9, E.H., Rebollo, T.C.: A multilayer method for the hydrostatic Navier\u2013Stokes equations: a particular weak solution. J. Sci. Comput. 60(2), 408\u2013437 (2013). https:\/\/doi.org\/10.1007\/s10915-013-9802-0","journal-title":"J. Sci. Comput."},{"issue":"5","key":"2299_CR40","doi-asserted-by":"publisher","first-page":"1169","DOI":"10.4310\/cms.2018.v16.n5.a1","volume":"16","author":"ED Fern\u00e1ndez-Nieto","year":"2018","unstructured":"Fern\u00e1ndez-Nieto, E.D., Parisot, M., Penel, Y., Sainte-Marie, J.: A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows. Commun. Math. Sci. 16(5), 1169\u20131202 (2018). https:\/\/doi.org\/10.4310\/cms.2018.v16.n5.a1","journal-title":"Commun. Math. Sci."},{"issue":"1","key":"2299_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jnnfm.2005.01.003","volume":"127","author":"I Frigaard","year":"2005","unstructured":"Frigaard, I., Nouar, C.: On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J. Nonnewton. Fluid Mech. 127(1), 1\u201326 (2005). https:\/\/doi.org\/10.1016\/j.jnnfm.2005.01.003","journal-title":"J. Nonnewton. Fluid Mech."},{"key":"2299_CR42","doi-asserted-by":"publisher","unstructured":"Garres-D\u00edaz, J., Fern\u00e1ndez-Nieto, E.D., Mangeney, A., Morales de Luna, T.: A weakly non-hydrostatic shallow model for dry granular flows. J. Sci. Comput. (2021). https:\/\/doi.org\/10.1007\/s10915-020-01377-9","DOI":"10.1007\/s10915-020-01377-9"},{"issue":"4","key":"2299_CR43","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1140\/epje\/i2003-10153-0","volume":"14","author":"GDR MiDi","year":"2004","unstructured":"MiDi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14(4), 341\u2013365 (2004). https:\/\/doi.org\/10.1140\/epje\/i2003-10153-0","journal-title":"Eur. Phys. J. E"},{"key":"2299_CR44","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.compfluid.2019.05.012","volume":"188","author":"L Gesenhues","year":"2019","unstructured":"Gesenhues, L., Camata, J.J., C\u00f4rtes, A.M., Rochinha, F.A., Coutinho, A.: Finite element simulation of complex dense granular flows using a well-posed regularization of the $$\\mu $$(I)-rheology. Comput. Fluids 188, 102\u2013113 (2019). https:\/\/doi.org\/10.1016\/j.compfluid.2019.05.012","journal-title":"Comput. Fluids"},{"key":"2299_CR45","unstructured":"Glowinski, R., Lions, J.L., Tr\u00e9moli\u00e8res, R.: Analyse num\u00e9rique des in\u00e9quations variationnelles (Tomes 1 et 2). Bordas (Dunod) (1976)"},{"key":"2299_CR46","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1017\/jfm.2014.450","volume":"755","author":"JMNT Gray","year":"2014","unstructured":"Gray, J.M.N.T., Edwards, A.N.: A depth-averaged $$\\mu $$(I)-rheology for shallow granular free-surface flows. J. Fluid Mech. 755, 503\u2013534 (2014). https:\/\/doi.org\/10.1017\/jfm.2014.450","journal-title":"J. Fluid Mech."},{"issue":"1\u20132","key":"2299_CR47","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10665-009-9328-5","volume":"67","author":"G Grosso","year":"2009","unstructured":"Grosso, G., Antuono, M., Brocchini, M.: Dispersive nonlinear shallow-water equations: some preliminary numerical results. J. Eng. Math. 67(1\u20132), 71\u201384 (2009). https:\/\/doi.org\/10.1007\/s10665-009-9328-5","journal-title":"J. Eng. Math."},{"key":"2299_CR48","doi-asserted-by":"publisher","first-page":"P1","DOI":"10.1017\/jfm.2018.548","volume":"852","author":"E Guazzelli","year":"2018","unstructured":"Guazzelli, E., Pouliquen, O.: Rheology of dense granular suspensions. J. Fluid Mech. 852, P1 (2018). https:\/\/doi.org\/10.1017\/jfm.2018.548","journal-title":"J. Fluid Mech."},{"issue":"44\u201347","key":"2299_CR49","doi-asserted-by":"publisher","first-page":"6011","DOI":"10.1016\/j.cma.2005.10.010","volume":"195","author":"J Guermond","year":"2006","unstructured":"Guermond, J., Minev, P., Shen, J.: An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195(44\u201347), 6011\u20136045 (2006). https:\/\/doi.org\/10.1016\/j.cma.2005.10.010","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2299_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.108917","volume":"399","author":"JL Guermond","year":"2019","unstructured":"Guermond, J.L., Popov, B., Tovar, E., Kees, C.: Robust explicit relaxation technique for solving the Green-Naghdi equations. J. Comput. Phys. 399, 108917 (2019). https:\/\/doi.org\/10.1016\/j.jcp.2019.108917","journal-title":"J. Comput. Phys."},{"key":"2299_CR51","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1017\/jfm.2017.612","volume":"830","author":"J Heyman","year":"2017","unstructured":"Heyman, J., Delannay, R., Tabuteau, H., Valance, A.: Compressibility regularizes the $$\\mu $$(I)-rheology for dense granular flows. J. Fluid Mech. 830, 553\u2013568 (2017). https:\/\/doi.org\/10.1017\/jfm.2017.612","journal-title":"J. Fluid Mech."},{"key":"2299_CR52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jnnfm.2015.02.006","volume":"219","author":"IR Ionescu","year":"2015","unstructured":"Ionescu, I.R., Mangeney, A., Bouchut, F., Roche, R.: Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J. Nonnewton. Fluid Mech. 219, 1\u201318 (2015). https:\/\/doi.org\/10.1016\/j.jnnfm.2015.02.006","journal-title":"J. Nonnewton. Fluid Mech."},{"issue":"7094","key":"2299_CR53","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1038\/nature04801","volume":"441","author":"P Jop","year":"2006","unstructured":"Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441(7094), 727\u2013730 (2006). https:\/\/doi.org\/10.1038\/nature04801","journal-title":"Nature"},{"issue":"8","key":"2299_CR54","doi-asserted-by":"publisher","DOI":"10.1063\/1.2753111","volume":"19","author":"P Jop","year":"2007","unstructured":"Jop, P., Forterre, Y., Pouliquen, O.: Initiation of granular surface flows in a narrow channel. Phys. Fluids 19(8), 088102 (2007). https:\/\/doi.org\/10.1063\/1.2753111","journal-title":"Phys. Fluids"},{"key":"2299_CR55","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1017\/jfm.2011.335","volume":"686","author":"PY Lagr\u00e9e","year":"2011","unstructured":"Lagr\u00e9e, P.Y., Staron, L., Popinet, S.: The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes with a $$\\mu $$(I)-rheology. J. Fluid Mech. 686, 378\u2013408 (2011). https:\/\/doi.org\/10.1017\/jfm.2011.335","journal-title":"J. Fluid Mech."},{"key":"2299_CR56","doi-asserted-by":"crossref","unstructured":"Lusso, C., Bouchut, F., Ern, A., Mangeney, A.: A free interface model for static\/flowing dynamics in thin-layer flows of granular materials with yield: Simple shear simulations and comparison with experiments. Appl. Sci. 7(4) (2017). http:\/\/www.mdpi.com\/2076-3417\/7\/4\/386","DOI":"10.3390\/app7040386"},{"key":"2299_CR57","doi-asserted-by":"publisher","unstructured":"Lusso, C., Bouchut, F., Ern, A., Mangeney, A.: Explicit solutions to a free interface model for the static\/flowing transition in thin granular flows. ESAIM: Math. Model. Numer. Anal. 55, S369\u2013S395 (2021). https:\/\/doi.org\/10.1051\/m2an\/2020042","DOI":"10.1051\/m2an\/2020042"},{"key":"2299_CR58","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/j.jcp.2016.12.036","volume":"333","author":"C Lusso","year":"2017","unstructured":"Lusso, C., Ern, A., Bouchut, F., Mangeney, A., Farin, M., Roche, O.: Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse. J. Comput. Phys. 333, 387\u2013408 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2016.12.036","journal-title":"J. Comput. Phys."},{"key":"2299_CR59","doi-asserted-by":"publisher","DOI":"10.5194\/nhess-2020-171","author":"J Mac\u00edas","year":"2021","unstructured":"Mac\u00edas, J., Escalante, C., Castro, M.: Multilayer-HySEA model validation for landslide generated tsunamis Part I. Rigid slides. Nat. Hazards Earth Syst. Sci. Discuss. (2021). https:\/\/doi.org\/10.5194\/nhess-2020-171","journal-title":"Nat. Hazards Earth Syst. Sci. Discuss."},{"key":"2299_CR60","doi-asserted-by":"publisher","unstructured":"Mangeney, A., Bouchut, F., Thomas, N., Vilotte, J.P., Bristeau, M.O.: Numerical modeling of self-channeling granular flows and of their levee-channel deposits. J. Geophys. Res.: Earth Surface 112(F2), (2007). https:\/\/doi.org\/10.1029\/2006JF000469","DOI":"10.1029\/2006JF000469"},{"key":"2299_CR61","doi-asserted-by":"publisher","unstructured":"Mangeney, A., Roche, O., Hungr, O., Mangold, N., Faccanoni, G., Lucas, A.: Erosion and mobility in granular collapse over sloping beds. J. Geophys. Res. 115(F3) (2010). https:\/\/doi.org\/10.1029\/2009jf001462","DOI":"10.1029\/2009jf001462"},{"key":"2299_CR62","doi-asserted-by":"publisher","unstructured":"Mangeney-Castelnau, A., Vilotte, J.P., Bristeau, M.O., Perthame, B., Bouchut, F., Simeoni, C., Yerneni, S.: Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme. J. Geophys. Res.: Solid Earth 108(B11) (2003). https:\/\/doi.org\/10.1029\/2002JB002024","DOI":"10.1029\/2002JB002024"},{"issue":"1","key":"2299_CR63","doi-asserted-by":"publisher","DOI":"10.1063\/1.4971320","volume":"29","author":"N Martin","year":"2017","unstructured":"Martin, N., Ionescu, I.R., Mangeney, A., Bouchut, F., Farin, M.: Continuum viscoplastic simulation of a granular column collapse on large slopes: $$\\mu $$(I) rheology and lateral wall effects. Phys. Fluids 29(1), 013301 (2017). https:\/\/doi.org\/10.1063\/1.4971320","journal-title":"Phys. Fluids"},{"issue":"2","key":"2299_CR64","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s00791-014-0223-x","volume":"16","author":"E M\u00fcller","year":"2013","unstructured":"M\u00fcller, E., Guo, X., Scheichl, R., Shi, S.: Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs. Comput. Vis. Sci. 16(2), 41\u201358 (2013)","journal-title":"Comput. Vis. Sci."},{"issue":"11","key":"2299_CR65","doi-asserted-by":"publisher","DOI":"10.1063\/1.3013896","volume":"20","author":"M Pailha","year":"2008","unstructured":"Pailha, M., Nicolas, M., Pouliquen, O.: Initiation of underwater granular avalanches: Influence of the initial volume fraction. Phys. Fluids 20(11), 111701 (2008). https:\/\/doi.org\/10.1063\/1.3013896","journal-title":"Phys. Fluids"},{"issue":"5","key":"2299_CR66","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1122\/1.549926","volume":"31","author":"T Papanastasiou","year":"1987","unstructured":"Papanastasiou, T.: Flows of Materials with Yield. J. Rheol. 31(5), 385\u2013404 (1987). https:\/\/doi.org\/10.1122\/1.549926","journal-title":"J. Rheol."},{"issue":"04","key":"2299_CR67","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1017\/S0022112067002605","volume":"27","author":"D Peregrine","year":"1967","unstructured":"Peregrine, D.: Long waves on a beach. J. Fluid Mech. 27(04), 815\u2013827 (1967)","journal-title":"J. Fluid Mech."},{"key":"2299_CR68","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-49507-0","author":"M Peruzzetto","year":"2019","unstructured":"Peruzzetto, M., Komorowski, J.C., Le Friant, A., Rosas-Carbajal, M., Mangeney, A., Legendre, Y.: Modeling of partial dome collapse of La Soufri\u00e8re of Guadeloupe volcano: implications for hazard assessment and monitoring. Sci. Rep. (2019). https:\/\/doi.org\/10.1038\/s41598-019-49507-0","journal-title":"Sci. Rep."},{"key":"2299_CR69","doi-asserted-by":"publisher","DOI":"10.1016\/j.enggeo.2021.106457","volume":"296","author":"M Peruzzetto","year":"2022","unstructured":"Peruzzetto, M., Levy, C., Thiery, Y., Grandjean, G., Mangeney, A., Lejeune, A.M., Nachbaur, A., Legendre, Y., Vittecoq, B., Saurel, J.M., Clouard, V., Dewez, T., Fontaine, F.R., Mergili, M., Lagarde, S., Komorowski, J., Friant, A.L., Lemarchand, A.: Simplified simulation of rock avalanches and subsequent debris flows with a single thin-layer model: Application to the Pr\u00eacheur river (Martinique, Lesser Antilles). Eng. Geol. 296, 106457 (2022). https:\/\/doi.org\/10.1016\/j.enggeo.2021.106457","journal-title":"Eng. Geol."},{"key":"2299_CR70","doi-asserted-by":"publisher","DOI":"10.1029\/2020jf005657","author":"M Peruzzetto","year":"2021","unstructured":"Peruzzetto, M., Mangeney, A., Bouchut, F., Grandjean, G., Levy, C., Thiery, Y., Lucas, A.: Topography curvature effects in thin-layer models for gravity-driven flows without bed erosion. J. Geophys. Res.: Earth Surface (2021). https:\/\/doi.org\/10.1029\/2020jf005657","journal-title":"J. Geophys. Res.: Earth Surface"},{"issue":"11","key":"2299_CR71","doi-asserted-by":"publisher","first-page":"424","DOI":"10.3390\/geosciences10110424","volume":"10","author":"M Peruzzetto","year":"2020","unstructured":"Peruzzetto, M., Mangeney, A., Grandjean, G., Levy, C., Thiery, Y., Rohmer, J., Lucas, A.: Operational estimation of landslide runout: comparison of empirical and numerical methods. Geosciences 10(11), 424 (2020). https:\/\/doi.org\/10.3390\/geosciences10110424","journal-title":"Geosciences"},{"issue":"1","key":"2299_CR72","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s00603-007-0143-x","volume":"41","author":"M Pirulli","year":"2008","unstructured":"Pirulli, M., Mangeney, A.: Results of back-analysis of the propagation of rock avalanches as a function of the assumed rheology. Rock Mech. Rock Eng. 41(1), 59\u201384 (2008). https:\/\/doi.org\/10.1007\/s00603-007-0143-x","journal-title":"Rock Mech. Rock Eng."},{"issue":"7","key":"2299_CR73","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1063\/1.870057","volume":"11","author":"O Pouliquen","year":"1999","unstructured":"Pouliquen, O.: On the shape of granular fronts down rough inclined planes. Phys. Fluids 11(7), 1956\u20131958 (1999). https:\/\/doi.org\/10.1063\/1.870057","journal-title":"Phys. Fluids"},{"issue":"3","key":"2299_CR74","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1063\/1.869928","volume":"11","author":"O Pouliquen","year":"1999","unstructured":"Pouliquen, O.: Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11(3), 542\u2013548 (1999). https:\/\/doi.org\/10.1063\/1.869928","journal-title":"Phys. Fluids"},{"key":"2299_CR75","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1017\/s0022112001006796","volume":"453","author":"O Pouliquen","year":"2002","unstructured":"Pouliquen, O., Forterre, Y.: Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 453, 133\u2013151 (2002). https:\/\/doi.org\/10.1017\/s0022112001006796","journal-title":"J. Fluid Mech."},{"issue":"1909","key":"2299_CR76","doi-asserted-by":"publisher","first-page":"5091","DOI":"10.1098\/rsta.2009.0171","volume":"367","author":"O Pouliquen","year":"2009","unstructured":"Pouliquen, O., Forterre, Y.: A non-local rheology for dense granular flows. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 367(1909), 5091\u20135107 (2009). https:\/\/doi.org\/10.1098\/rsta.2009.0171","journal-title":"Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci."},{"key":"2299_CR77","doi-asserted-by":"publisher","unstructured":"Rauter, M.: The compressible granular collapse in a fluid as a continuum: validity of a Navier\u2013Stokes model with $$\\mu $$(I)-rheology. J. Fluid Mech. 915 (2021). https:\/\/doi.org\/10.1017\/jfm.2021.107","DOI":"10.1017\/jfm.2021.107"},{"key":"2299_CR78","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2020.103492","volume":"122","author":"M Rauter","year":"2020","unstructured":"Rauter, M., Barker, T., Fellin, W.: Granular viscosity from plastic yield surfaces: the role of the deformation type in granular flows. Comput. Geotech. 122, 103492 (2020). https:\/\/doi.org\/10.1016\/j.compgeo.2020.103492","journal-title":"Comput. Geotech."},{"key":"2299_CR79","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1017\/S0022112089000340","volume":"199","author":"SB Savage","year":"1989","unstructured":"Savage, S.B., Hutter, K.: The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177\u2013215 (1989). https:\/\/doi.org\/10.1017\/S0022112089000340","journal-title":"J. Fluid Mech."},{"key":"2299_CR80","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1017\/jfm.2019.476","volume":"874","author":"DG Schaeffer","year":"2019","unstructured":"Schaeffer, D.G., Barker, T., Tsuji, D., Gremaud, P., Shearer, M., Gray, J.M.N.T.: Constitutive relations for compressible granular flow in the inertial regime. J. Fluid Mech. 874, 926\u2013951 (2019). https:\/\/doi.org\/10.1017\/jfm.2019.476","journal-title":"J. Fluid Mech."},{"issue":"7","key":"2299_CR81","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1002\/(sici)1097-0363(19960415)22:7<581::aid-fld365>3.0.co;2-r","volume":"22","author":"M Thomadakis","year":"1996","unstructured":"Thomadakis, M., Leschziner, M.: A pressure-correction method for the solution of incompressible viscous flows on unsctructured grids. Int. J. Numer. Meth. Fluids 22(7), 581\u2013601 (1996). https:\/\/doi.org\/10.1002\/(sici)1097-0363(19960415)22:7<581::aid-fld365>3.0.co;2-r","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"2299_CR82","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1002\/fld.1952","volume":"61","author":"Y Yamazaki","year":"2008","unstructured":"Yamazaki, Y., Kowalik, Z., Cheung, K.F.: Depth-integrated, non-hydrostatic model for wave breaking and run-up. Numer. Methods Fluids 61, 473\u2013497 (2008). https:\/\/doi.org\/10.1002\/fld.1952","journal-title":"Numer. Methods Fluids"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02299-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02299-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02299-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T11:16:25Z","timestamp":1692616585000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02299-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,7]]},"references-count":82,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["2299"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02299-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2023,8,7]]},"assertion":[{"value":"6 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 May 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"88"}}