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Volumn 302, Issue , 2015, Pages 336-358

A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations

Author keywords

Adaptive mesh refinement; Dispersive wave model; Multigrid elliptic solver; Quadtree; Tsunami; Well balanced

Indexed keywords

DISPERSION (WAVES); LINEAR SYSTEMS; MESH GENERATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; TSUNAMIS;

EID: 84942284104     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2015.09.009     Document Type: Article
Times cited : (282)

References (52)
  • 1
    • 4644342716 scopus 로고    scopus 로고
    • A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
    • Audusse E., Bouchut F., Bristeau M.-O., Klein R., Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 2004, 25(6):2050-2065.
    • (2004) SIAM J. Sci. Comput. , vol.25 , Issue.6 , pp. 2050-2065
    • Audusse, E.1    Bouchut, F.2    Bristeau, M.-O.3    Klein, R.4    Perthame, B.5
  • 2
    • 80052830830 scopus 로고    scopus 로고
    • The GeoClaw software for depth-averaged flows with adaptive refinement
    • Berger M.J., George D.L., LeVeque R.J., Mandli K.T. The GeoClaw software for depth-averaged flows with adaptive refinement. Adv. Water Resour. 2011, 34(9):1195-1206.
    • (2011) Adv. Water Resour. , vol.34 , Issue.9 , pp. 1195-1206
    • Berger, M.J.1    George, D.L.2    LeVeque, R.J.3    Mandli, K.T.4
  • 3
    • 0020167657 scopus 로고
    • Verification of numerical wave propagation models for simple harmonic linear water waves
    • Berkhoff J.C.W., Booy N., Radder A.C. Verification of numerical wave propagation models for simple harmonic linear water waves. Coast. Eng. 1982, 6(3):255-279.
    • (1982) Coast. Eng. , vol.6 , Issue.3 , pp. 255-279
    • Berkhoff, J.C.W.1    Booy, N.2    Radder, A.C.3
  • 4
    • 78650568860 scopus 로고    scopus 로고
    • A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
    • Bonneton P., Chazel F., Lannes D., Marche F., Tissier M. A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model. J. Comput. Phys. 2011, 230:1479-1498.
    • (2011) J. Comput. Phys. , vol.230 , pp. 1479-1498
    • Bonneton, P.1    Chazel, F.2    Lannes, D.3    Marche, F.4    Tissier, M.5
  • 6
    • 39549099929 scopus 로고    scopus 로고
    • Nonlinear shallow water equation modeling for coastal engineering
    • Brocchini M., Dodd N. Nonlinear shallow water equation modeling for coastal engineering. J. Waterw. Port Coast. Ocean Eng. 2008, 134(2):104-120.
    • (2008) J. Waterw. Port Coast. Ocean Eng. , vol.134 , Issue.2 , pp. 104-120
    • Brocchini, M.1    Dodd, N.2
  • 7
    • 33746360902 scopus 로고    scopus 로고
    • A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis
    • Cienfuegos R., Barthelemy E., Bonneton P. A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis. Int. J. Numer. Methods Fluids 2006, 51(11):1217-1253.
    • (2006) Int. J. Numer. Methods Fluids , vol.51 , Issue.11 , pp. 1217-1253
    • Cienfuegos, R.1    Barthelemy, E.2    Bonneton, P.3
  • 8
    • 33947224160 scopus 로고    scopus 로고
    • A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: boundary conditions and validation
    • Cienfuegos R., Barthelemy E., Bonneton P. A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: boundary conditions and validation. Int. J. Numer. Methods Fluids 2007, 53(9):1423-1456.
    • (2007) Int. J. Numer. Methods Fluids , vol.53 , Issue.9 , pp. 1423-1456
    • Cienfuegos, R.1    Barthelemy, E.2    Bonneton, P.3
  • 9
    • 84961288277 scopus 로고    scopus 로고
    • Discontinuous-Galerkin discretization of a new class of Green-Naghdi equations
    • Duran A., Marche F. Discontinuous-Galerkin discretization of a new class of Green-Naghdi equations. Commun. Comput. Phys. 2015, 17(03):721-760.
    • (2015) Commun. Comput. Phys. , vol.17 , Issue.3 , pp. 721-760
    • Duran, A.1    Marche, F.2
  • 10
    • 84883170138 scopus 로고    scopus 로고
    • Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations
    • Dutykh D., Clamond D., Milewski P., Mitsotakis D. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. Eur. J. Appl. Math. 2013, 24(05):761-787.
    • (2013) Eur. J. Appl. Math. , vol.24 , Issue.5 , pp. 761-787
    • Dutykh, D.1    Clamond, D.2    Milewski, P.3    Mitsotakis, D.4
  • 11
    • 36549000207 scopus 로고    scopus 로고
    • Simulation of nonlinear wave run-up with a high-order Boussinesq model
    • Fuhrman D.R., Madsen P.A. Simulation of nonlinear wave run-up with a high-order Boussinesq model. Coast. Eng. 2008, 55(2):139-154.
    • (2008) Coast. Eng. , vol.55 , Issue.2 , pp. 139-154
    • Fuhrman, D.R.1    Madsen, P.A.2
  • 12
    • 79958852332 scopus 로고    scopus 로고
    • High-resolution methods and adaptive refinement for tsunami propagation and inundation
    • Springer
    • George D.L., LeVeque R.J. High-resolution methods and adaptive refinement for tsunami propagation and inundation. Hyperbolic Problems: Theory, Numerics, Applications 2008, 541-549. Springer.
    • (2008) Hyperbolic Problems: Theory, Numerics, Applications , pp. 541-549
    • George, D.L.1    LeVeque, R.J.2
  • 14
    • 0016876595 scopus 로고
    • A derivation of equations for wave propagation in water of variable depth
    • Green A.E., Naghdi P.M. A derivation of equations for wave propagation in water of variable depth. J. Fluid Mech. 1976, 78(02):237-246.
    • (1976) J. Fluid Mech. , vol.78 , Issue.2 , pp. 237-246
    • Green, A.E.1    Naghdi, P.M.2
  • 15
    • 77958017327 scopus 로고    scopus 로고
    • Numerical simulation and first-order hazard analysis of large co-seismic tsunamis generated in the Puerto Rico trench: near-field impact on the north shore of Puerto Rico and far-field impact on the US east coast
    • Grilli S.T., Dubosq S., Pophet N., Pérignon Y., Kirby J.T., Shi F. Numerical simulation and first-order hazard analysis of large co-seismic tsunamis generated in the Puerto Rico trench: near-field impact on the north shore of Puerto Rico and far-field impact on the US east coast. Nat. Hazards Earth Syst. Sci. 2010, 10(10):2109-2125.
    • (2010) Nat. Hazards Earth Syst. Sci. , vol.10 , Issue.10 , pp. 2109-2125
    • Grilli, S.T.1    Dubosq, S.2    Pophet, N.3    Pérignon, Y.4    Kirby, J.T.5    Shi, F.6
  • 16
    • 34648834227 scopus 로고    scopus 로고
    • A cache-aware algorithm for PDEs on hierarchical data structures based on space-filling curves
    • Günther F., Mehl M., Pögl M., Zenger C. A cache-aware algorithm for PDEs on hierarchical data structures based on space-filling curves. SIAM J. Sci. Comput. 2006, 28(5):1634-1650.
    • (2006) SIAM J. Sci. Comput. , vol.28 , Issue.5 , pp. 1634-1650
    • Günther, F.1    Mehl, M.2    Pögl, M.3    Zenger, C.4
  • 17
    • 0442281584 scopus 로고    scopus 로고
    • Modeling mesoscale turbulence in the barotropic double-gyre circulation
    • Holm D.D., Nadiga B.T. Modeling mesoscale turbulence in the barotropic double-gyre circulation. J. Phys. Oceanogr. 2003, 33(11):2355-2365.
    • (2003) J. Phys. Oceanogr. , vol.33 , Issue.11 , pp. 2355-2365
    • Holm, D.D.1    Nadiga, B.T.2
  • 18
    • 33750107470 scopus 로고    scopus 로고
    • Wave dispersion study in the Indian Ocean tsunami of December 26, 2004
    • Horrillo J., Kowalik Z., Shigihara Y. Wave dispersion study in the Indian Ocean tsunami of December 26, 2004. Mar. Geod. 2006, 29(3):149-166.
    • (2006) Mar. Geod. , vol.29 , Issue.3 , pp. 149-166
    • Horrillo, J.1    Kowalik, Z.2    Shigihara, Y.3
  • 19
    • 84878741505 scopus 로고    scopus 로고
    • A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains
    • Hou J., Liang Q., Simons F., Hinkelmann R. A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains. Comput. Fluids 2013, 82:132-147.
    • (2013) Comput. Fluids , vol.82 , pp. 132-147
    • Hou, J.1    Liang, Q.2    Simons, F.3    Hinkelmann, R.4
  • 21
    • 84862656431 scopus 로고    scopus 로고
    • An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations
    • Kazolea M., Delis A.I., Nikolos I.K., Synolakis C.E. An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations. Coast. Eng. 2012, 69:42-66.
    • (2012) Coast. Eng. , vol.69 , pp. 42-66
    • Kazolea, M.1    Delis, A.I.2    Nikolos, I.K.3    Synolakis, C.E.4
  • 22
    • 84872379239 scopus 로고    scopus 로고
    • Dispersive tsunami waves in the ocean: model equations and sensitivity to dispersion and Coriolis effects
    • Kirby J.T., Shi F., Tehranirad B., Harris J.C., Grilli S.T. Dispersive tsunami waves in the ocean: model equations and sensitivity to dispersion and Coriolis effects. Ocean Model. 2013, 62:39-55.
    • (2013) Ocean Model. , vol.62 , pp. 39-55
    • Kirby, J.T.1    Shi, F.2    Tehranirad, B.3    Harris, J.C.4    Grilli, S.T.5
  • 23
    • 46849105352 scopus 로고    scopus 로고
    • Dispersion of the Sumatra tsunami waves in the Indian Ocean detected by satellite altimetry
    • Kulikov E. Dispersion of the Sumatra tsunami waves in the Indian Ocean detected by satellite altimetry. Russ. J. Earth Sci. 2006, 8.
    • (2006) Russ. J. Earth Sci. , vol.8
    • Kulikov, E.1
  • 24
    • 59649093678 scopus 로고    scopus 로고
    • Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
    • Lannes D., Bonneton P. Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation. Phys. Fluids 2009, 21(1):16601.
    • (2009) Phys. Fluids , vol.21 , Issue.1 , pp. 16601
    • Lannes, D.1    Bonneton, P.2
  • 25
    • 84913553436 scopus 로고    scopus 로고
    • A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations
    • Lannes D., Marche F. A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations. J. Comput. Phys. 2015, 282:238-268.
    • (2015) J. Comput. Phys. , vol.282 , pp. 238-268
    • Lannes, D.1    Marche, F.2
  • 26
    • 84906917391 scopus 로고    scopus 로고
    • High-resolution finite volume methods for the shallow water equations with bathymetry and dry states
    • LeVeque R.J., George D.L. High-resolution finite volume methods for the shallow water equations with bathymetry and dry states. Proceedings of Long-Wave Workshop 2004.
    • (2004) Proceedings of Long-Wave Workshop
    • LeVeque, R.J.1    George, D.L.2
  • 27
    • 79956136824 scopus 로고    scopus 로고
    • Tsunami modelling with adaptively refined finite volume methods
    • LeVeque R.J., George D.L., Berger M.J. Tsunami modelling with adaptively refined finite volume methods. Acta Numer. 2011, 20:211-289.
    • (2011) Acta Numer. , vol.20 , pp. 211-289
    • LeVeque, R.J.1    George, D.L.2    Berger, M.J.3
  • 28
    • 84886260329 scopus 로고    scopus 로고
    • High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
    • Li M., Guyenne P., Li F., Xu L. High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model. J. Comput. Phys. 2014, 257:169-192.
    • (2014) J. Comput. Phys. , vol.257 , pp. 169-192
    • Li, M.1    Guyenne, P.2    Li, F.3    Xu, L.4
  • 29
    • 4344607336 scopus 로고    scopus 로고
    • Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids
    • Liang Q., Borthwick A.G.L., Stelling G. Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids. Int. J. Numer. Methods Fluids 2004, 46(2):127-162.
    • (2004) Int. J. Numer. Methods Fluids , vol.46 , Issue.2 , pp. 127-162
    • Liang, Q.1    Borthwick, A.G.L.2    Stelling, G.3
  • 31
    • 33645878917 scopus 로고    scopus 로고
    • A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry
    • Madsen P.A., Fuhrman D.R., Wang B. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 2006, 53(5-6):487-504.
    • (2006) Coast. Eng. , vol.53 , Issue.5-6 , pp. 487-504
    • Madsen, P.A.1    Fuhrman, D.R.2    Wang, B.3
  • 32
    • 84906951164 scopus 로고    scopus 로고
    • On the Galerkin/finite-element method for the Serre equations
    • Mitsotakis D., Ilan B. On the Galerkin/finite-element method for the Serre equations. J. Sci. Comput. 2014, 61:166-195.
    • (2014) J. Sci. Comput. , vol.61 , pp. 166-195
    • Mitsotakis, D.1    Ilan, B.2
  • 33
    • 73649106498 scopus 로고    scopus 로고
    • A numerical scheme for the Green-Naghdi model
    • Le Métayer O., Gavrilyuk S., Hank S. A numerical scheme for the Green-Naghdi model. J. Comput. Phys. 2010, 229:2034-2045.
    • (2010) J. Comput. Phys. , vol.229 , pp. 2034-2045
    • Le Métayer, O.1    Gavrilyuk, S.2    Hank, S.3
  • 34
    • 0030209434 scopus 로고    scopus 로고
    • Different approximations of shallow fluid over an obstacle
    • Nadiga B.T., Margolin L.G., Smolarkiewicz P.K. Different approximations of shallow fluid over an obstacle. Phys. Fluids 1996, 8(8):2066-2077.
    • (1996) Phys. Fluids , vol.8 , Issue.8 , pp. 2066-2077
    • Nadiga, B.T.1    Margolin, L.G.2    Smolarkiewicz, P.K.3
  • 35
    • 70349410335 scopus 로고    scopus 로고
    • An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography
    • Nikolos I.K., Delis A.I. An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography. Comput. Methods Appl. Mech. Eng. 2009, 198(47):3723-3750.
    • (2009) Comput. Methods Appl. Mech. Eng. , vol.198 , Issue.47 , pp. 3723-3750
    • Nikolos, I.K.1    Delis, A.I.2
  • 36
    • 0027789687 scopus 로고
    • Alternative form of Boussinesq equations for nearshore wave propagation
    • Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterw. Port Coast. Ocean Eng. 1993, 119(6):618-638.
    • (1993) J. Waterw. Port Coast. Ocean Eng. , vol.119 , Issue.6 , pp. 618-638
    • Nwogu, O.1
  • 37
    • 0141515637 scopus 로고    scopus 로고
    • Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
    • Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 2003, 190(2):572-600.
    • (2003) J. Comput. Phys. , vol.190 , Issue.2 , pp. 572-600
    • Popinet, S.1
  • 39
    • 81255168239 scopus 로고    scopus 로고
    • Quadtree-adaptive tsunami modelling
    • Popinet S. Quadtree-adaptive tsunami modelling. Ocean Dyn. 2011, 61(9):1261-1285.
    • (2011) Ocean Dyn. , vol.61 , Issue.9 , pp. 1261-1285
    • Popinet, S.1
  • 40
    • 84860494435 scopus 로고    scopus 로고
    • Adaptive modelling of long-distance wave propagation and fine-scale flooding during the Tohoku tsunami
    • Popinet S. Adaptive modelling of long-distance wave propagation and fine-scale flooding during the Tohoku tsunami. Nat. Hazards Earth Syst. Sci. 2012, 12(4):1213-1227.
    • (2012) Nat. Hazards Earth Syst. Sci. , vol.12 , Issue.4 , pp. 1213-1227
    • Popinet, S.1
  • 46
    • 84966222159 scopus 로고
    • Krylov subspace methods for solving large unsymmetric linear systems
    • Saad Y. Krylov subspace methods for solving large unsymmetric linear systems. Math. Comput. 1981, 37(155):105-126.
    • (1981) Math. Comput. , vol.37 , Issue.155 , pp. 105-126
    • Saad, Y.1
  • 47
    • 84988999117 scopus 로고
    • Contribution à l'étude des écoulements permanents et variables dans les canaux
    • Serre F. Contribution à l'étude des écoulements permanents et variables dans les canaux. Houille Blanche 1953, 3:374-388.
    • (1953) Houille Blanche , vol.3 , pp. 374-388
    • Serre, F.1
  • 48
    • 84855748954 scopus 로고    scopus 로고
    • A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation
    • Shi F., Kirby J.T., Harris J.C., Geiman J.D., Grilli S.T. A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Model. 2012, 43:36-51.
    • (2012) Ocean Model. , vol.43 , pp. 36-51
    • Shi, F.1    Kirby, J.T.2    Harris, J.C.3    Geiman, J.D.4    Grilli, S.T.5
  • 50
    • 84860791117 scopus 로고    scopus 로고
    • A new approach to handle wave breaking in fully non-linear Boussinesq models
    • Tissier M., Bonneton P., Marche F., Chazel F., Lannes D. A new approach to handle wave breaking in fully non-linear Boussinesq models. Coast. Eng. 2012, 67:54-66.
    • (2012) Coast. Eng. , vol.67 , pp. 54-66
    • Tissier, M.1    Bonneton, P.2    Marche, F.3    Chazel, F.4    Lannes, D.5
  • 51
    • 15744402546 scopus 로고    scopus 로고
    • Coastal ocean models: two useful finite element methods
    • Walters R.A. Coastal ocean models: two useful finite element methods. Cont. Shelf Res. 2005, 25(7):775-793.
    • (2005) Cont. Shelf Res. , vol.25 , Issue.7 , pp. 775-793
    • Walters, R.A.1
  • 52
    • 0029343414 scopus 로고
    • A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
    • Wei G., Kirby J.T., Grilli S.T., Subramanya R. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. J. Fluid Mech. 1995, 294:71-92.
    • (1995) J. Fluid Mech. , vol.294 , pp. 71-92
    • Wei, G.1    Kirby, J.T.2    Grilli, S.T.3    Subramanya, R.4


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