Zefzouf, Meriem; Marche, Fabien A new symmetric interior penalty discontinuous Galerkin formulation for the Serre-Green-Naghdi equations. (English) Zbl 07776971 Numer. Methods Partial Differ. Equations 39, No. 2, 1478-1503 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{M. Zefzouf} and \textit{F. Marche}, Numer. Methods Partial Differ. Equations 39, No. 2, 1478--1503 (2023; Zbl 07776971) Full Text: DOI
Essama, Bedel Giscard Onana; Ngo Bisse, Jacquie Therese; Essiane, Salome Ndjakomo; Atangana, Jacques Generation of double Sasa-Satsuma, double Kuznetsov-Ma and other exotic solutions of cubic-quintic Ginzburg-Landau equation in a left-handed material. (English) Zbl 1524.35493 Wave Motion 120, Article ID 103143, 18 p. (2023). MSC: 35Q40 65M99 PDFBibTeX XMLCite \textit{B. G. O. Essama} et al., Wave Motion 120, Article ID 103143, 18 p. (2023; Zbl 1524.35493) Full Text: DOI
Pitt, Jordan P. A.; Zoppou, Christopher; Roberts, Stephen G. Numerical scheme for the generalised Serre-Green-Naghdi model. (English) Zbl 1524.76245 Wave Motion 115, Article ID 103077, 20 p. (2022). MSC: 76M12 65M08 76U60 PDFBibTeX XMLCite \textit{J. P. A. Pitt} et al., Wave Motion 115, Article ID 103077, 20 p. (2022; Zbl 1524.76245) Full Text: DOI
Duchêne, Vincent; Klein, Christian Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart. (English) Zbl 1503.65259 Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 5905-5933 (2022). Reviewer: Anouar Ben Mabrouk (Monastir) MSC: 65M70 65F10 65L06 35Q35 76B15 35B35 35C08 35B05 35B44 PDFBibTeX XMLCite \textit{V. Duchêne} and \textit{C. Klein}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 5905--5933 (2022; Zbl 1503.65259) Full Text: DOI arXiv
Lteif, Ralph; Gerbi, Stéphane A new class of higher-ordered/extended Boussinesq system for efficient numerical simulations by splitting operators. (English) Zbl 1510.76102 Appl. Math. Comput. 432, Article ID 127373, 30 p. (2022). MSC: 76M12 65M08 65M06 76B15 PDFBibTeX XMLCite \textit{R. Lteif} and \textit{S. Gerbi}, Appl. Math. Comput. 432, Article ID 127373, 30 p. (2022; Zbl 1510.76102) Full Text: DOI arXiv
Khorbatly, Bashar; Lteif, Ralph; Israwi, Samer; Gerbi, Stéphane Mathematical modeling and numerical analysis for the higher order Boussinesq system. (English) Zbl 1490.35327 ESAIM, Math. Model. Numer. Anal. 56, No. 2, 593-615 (2022). MSC: 35Q35 35L45 35L60 76B25 76B45 76B55 35C07 35B40 35A01 35A02 65L99 PDFBibTeX XMLCite \textit{B. Khorbatly} et al., ESAIM, Math. Model. Numer. Anal. 56, No. 2, 593--615 (2022; Zbl 1490.35327) Full Text: DOI arXiv
Israwi, Samer; Kalisch, Henrik; Katsaounis, Theodoros; Mitsotakis, Dimitrios A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis. (English) Zbl 1481.35331 Nonlinearity 35, No. 1, 750-786 (2022). MSC: 35Q35 76B15 35C08 35B65 35B45 35B40 65M60 65L06 65N30 65M12 65M15 PDFBibTeX XMLCite \textit{S. Israwi} et al., Nonlinearity 35, No. 1, 750--786 (2022; Zbl 1481.35331) Full Text: DOI arXiv
Robaux, Fabien; Benoit, Michel Development and validation of a numerical wave tank based on the harmonic polynomial cell and immersed boundary methods to model nonlinear wave-structure interaction. (English) Zbl 07516446 J. Comput. Phys. 446, Article ID 110560, 31 p. (2021). MSC: 76Mxx 76Bxx 65Mxx PDFBibTeX XMLCite \textit{F. Robaux} and \textit{M. Benoit}, J. Comput. Phys. 446, Article ID 110560, 31 p. (2021; Zbl 07516446) Full Text: DOI arXiv
Sánchez, Cipriano Escalante; Fernández-Nieto, Enrique D.; Morales de Luna, Tomás; Penel, Yohan; Sainte-Marie, Jacques Numerical simulations of a dispersive model approximating free-surface Euler equations. (English) Zbl 1502.65140 J. Sci. Comput. 89, No. 3, Paper No. 55, 35 p. (2021). MSC: 65M60 76B15 76B70 86A05 76M10 35Q31 35R35 PDFBibTeX XMLCite \textit{C. E. Sánchez} et al., J. Sci. Comput. 89, No. 3, Paper No. 55, 35 p. (2021; Zbl 1502.65140) Full Text: DOI
Ferrand, Martin; Harris, Jeffrey C. Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applications. (English) Zbl 1521.76418 Comput. Fluids 219, Article ID 104860, 17 p. (2021). MSC: 76M12 65M08 76U60 86A05 PDFBibTeX XMLCite \textit{M. Ferrand} and \textit{J. C. Harris}, Comput. Fluids 219, Article ID 104860, 17 p. (2021; Zbl 1521.76418) Full Text: DOI Link
Ranocha, Hendrik; Mitsotakis, Dimitrios; Ketcheson, David I. A broad class of conservative numerical methods for dispersive wave equations. (English) Zbl 1473.65154 Commun. Comput. Phys. 29, No. 4, 979-1029 (2021). MSC: 65M12 65M06 65M60 65M70 65M20 65L06 35Q35 76B15 PDFBibTeX XMLCite \textit{H. Ranocha} et al., Commun. Comput. Phys. 29, No. 4, 979--1029 (2021; Zbl 1473.65154) Full Text: DOI arXiv
Zhao, Jianli; Zhang, Qian; Yang, Yang; Xia, Yinhua Conservative discontinuous Galerkin methods for the nonlinear Serre equations. (English) Zbl 07508355 J. Comput. Phys. 421, Article ID 109729, 21 p. (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{J. Zhao} et al., J. Comput. Phys. 421, Article ID 109729, 21 p. (2020; Zbl 07508355) Full Text: DOI
Marche, Fabien Combined hybridizable discontinuous Galerkin (HDG) and Runge-Kutta discontinuous Galerkin (RK-DG) formulations for Green-Naghdi equations on unstructured meshes. (English) Zbl 07506187 J. Comput. Phys. 418, Article ID 109637, 33 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{F. Marche}, J. Comput. Phys. 418, Article ID 109637, 33 p. (2020; Zbl 07506187) Full Text: DOI HAL
Sari, Saida; Rowan, Thomas; Seaid, Mohammed; Benkhaldoun, Fayssal Simulation of three-dimensional free-surface flows using two-dimensional multilayer shallow water equations. (English) Zbl 1473.65143 Commun. Comput. Phys. 27, No. 5, 1413-1442 (2020). MSC: 65M08 35L53 76B15 74J40 76B07 PDFBibTeX XMLCite \textit{S. Sari} et al., Commun. Comput. Phys. 27, No. 5, 1413--1442 (2020; Zbl 1473.65143) Full Text: DOI
Klahn, Mathias; Madsen, Per A.; Fuhrman, David R. On the accuracy and applicability of a new implicit Taylor method and the high-order spectral method on steady nonlinear waves. (English) Zbl 1472.76065 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2243, Article ID 20200436, 27 p. (2020). MSC: 76M22 76B15 65M70 PDFBibTeX XMLCite \textit{M. Klahn} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2243, Article ID 20200436, 27 p. (2020; Zbl 1472.76065) Full Text: DOI Link
Dehghan, Mehdi; Abbaszadeh, Mostafa The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving Kriging interpolation shape functions with the weighted essentially non-oscillatory method. (English) Zbl 1524.65452 Commun. Nonlinear Sci. Numer. Simul. 68, 220-239 (2019). MSC: 65M08 35Q53 35B05 65D05 65M12 76B15 35Q35 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Commun. Nonlinear Sci. Numer. Simul. 68, 220--239 (2019; Zbl 1524.65452) Full Text: DOI
Papathanasiou, T. K.; Papoutsellis, Ch. E.; Athanassoulis, G. A. Semi-explicit solutions to the water-wave dispersion relation and their role in the non-linear Hamiltonian coupled-mode theory. (English) Zbl 07103641 J. Eng. Math. 114, 87-114 (2019). MSC: 65-XX 74-XX PDFBibTeX XMLCite \textit{T. K. Papathanasiou} et al., J. Eng. Math. 114, 87--114 (2019; Zbl 07103641) Full Text: DOI arXiv
Le, Uyen; Pelinovsky, Dmitry E. Convergence of Petviashvili’s method near periodic waves in the fractional Korteweg-de Vries equation. (English) Zbl 1419.35178 SIAM J. Math. Anal. 51, No. 4, 2850-2883 (2019). MSC: 35Q53 35P30 37K50 37K55 65J15 PDFBibTeX XMLCite \textit{U. Le} and \textit{D. E. Pelinovsky}, SIAM J. Math. Anal. 51, No. 4, 2850--2883 (2019; Zbl 1419.35178) Full Text: DOI arXiv
Bremer, Maximilian; Kazhyken, Kazbek; Kaiser, Hartmut; Michoski, Craig; Dawson, Clint Performance comparison of HPX versus traditional parallelization strategies for the discontinuous Galerkin method. (English) Zbl 1427.65238 J. Sci. Comput. 80, No. 2, 878-902 (2019). MSC: 65M60 65Y10 76B15 76M10 PDFBibTeX XMLCite \textit{M. Bremer} et al., J. Sci. Comput. 80, No. 2, 878--902 (2019; Zbl 1427.65238) Full Text: DOI
Khakimzyanov, Gayaz; Dutykh, Denys; Gusev, Oleg; Shokina, Nina Yu. Dispersive shallow water wave modelling. II: Numerical simulation on a globally flat space. (English) Zbl 1488.76020 Commun. Comput. Phys. 23, No. 1, 30-92 (2018). MSC: 76B15 76M12 65N08 65N06 PDFBibTeX XMLCite \textit{G. Khakimzyanov} et al., Commun. Comput. Phys. 23, No. 1, 30--92 (2018; Zbl 1488.76020) Full Text: DOI arXiv
Lawrence, C.; Adytia, D.; van Groesen, E. Variational Boussinesq model for strongly nonlinear dispersive waves. (English) Zbl 1524.86009 Wave Motion 76, 78-102 (2018). MSC: 86A05 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{C. Lawrence} et al., Wave Motion 76, 78--102 (2018; Zbl 1524.86009) Full Text: DOI
Duan, W. Y.; Wang, Z.; Zhao, B. B.; Ertekin, R. C.; Yang, W. Q. Steady solution of solitary wave and linear shear current interaction. (English) Zbl 1480.76020 Appl. Math. Modelling 60, 354-369 (2018). MSC: 76B25 65H10 PDFBibTeX XMLCite \textit{W. Y. Duan} et al., Appl. Math. Modelling 60, 354--369 (2018; Zbl 1480.76020) Full Text: DOI
Saleem, M. Rehan; Zia, Saqib; Ashraf, Waqas; Ali, Ishtiaq; Qamar, Shamsul The space-time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients. (English) Zbl 1409.76068 Comput. Math. Appl. 75, No. 3, 933-956 (2018). MSC: 76M10 65M60 76B15 35Q35 PDFBibTeX XMLCite \textit{M. R. Saleem} et al., Comput. Math. Appl. 75, No. 3, 933--956 (2018; Zbl 1409.76068) Full Text: DOI
Wang, Jinghua; Ma, Qingwei; Yan, Shiqiang A fully nonlinear numerical method for modeling wave-current interactions. (English) Zbl 1392.86033 J. Comput. Phys. 369, 173-190 (2018). MSC: 86A05 65Z05 65N38 35Q86 35Q35 PDFBibTeX XMLCite \textit{J. Wang} et al., J. Comput. Phys. 369, 173--190 (2018; Zbl 1392.86033) Full Text: DOI
Yan, Jinliang; Lai, Ming-Chih; Li, Zhilin; Zhang, Zhiyue New conservative finite volume element schemes for the modified regularized long wave equation. (English) Zbl 1488.65357 Adv. Appl. Math. Mech. 9, No. 2, 250-271 (2017). MSC: 65M08 74J35 65M06 65N08 65M12 35Q74 74S10 PDFBibTeX XMLCite \textit{J. Yan} et al., Adv. Appl. Math. Mech. 9, No. 2, 250--271 (2017; Zbl 1488.65357) Full Text: DOI
van Zwieten, J. S. B.; Sanderse, B.; Hendrix, M. H. W.; Vuik, C.; Henkes, R. A. W. M. Efficient simulation of one-dimensional two-phase flow with a high-order \(h\)-adaptive space-time discontinuous Galerkin method. (English) Zbl 1390.76388 Comput. Fluids 156, 34-47 (2017). MSC: 76M10 65M60 65M50 76Nxx 76T10 PDFBibTeX XMLCite \textit{J. S. B. van Zwieten} et al., Comput. Fluids 156, 34--47 (2017; Zbl 1390.76388) Full Text: DOI
Antonopoulos, D. C.; Dougalis, V. A.; Mitsotakis, D. E. Error estimates for Galerkin approximations of the Serre equations. (English) Zbl 1362.65099 SIAM J. Numer. Anal. 55, No. 2, 841-868 (2017); corrrigendum ibid. 59, No. 6, 3098-3101 (2021). MSC: 65M60 35Q53 PDFBibTeX XMLCite \textit{D. C. Antonopoulos} et al., SIAM J. Numer. Anal. 55, No. 2, 841--868 (2017; Zbl 1362.65099) Full Text: DOI arXiv
Maestre, Jorge; Cuesta, Ildefonso; Pallares, Jordi An unsteady 3D isogeometrical boundary element analysis applied to nonlinear gravity waves. (English) Zbl 1439.76118 Comput. Methods Appl. Mech. Eng. 310, 112-133 (2016). MSC: 76M15 65M38 76B15 65D17 65D07 PDFBibTeX XMLCite \textit{J. Maestre} et al., Comput. Methods Appl. Mech. Eng. 310, 112--133 (2016; Zbl 1439.76118) Full Text: DOI
Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios Mechanical balance laws for fully nonlinear and weakly dispersive water waves. (English) Zbl 1415.35010 Physica D 333, 243-253 (2016). MSC: 35B06 76B15 76L05 35C08 65M60 PDFBibTeX XMLCite \textit{H. Kalisch} et al., Physica D 333, 243--253 (2016; Zbl 1415.35010) Full Text: DOI arXiv
Zhou, B. Z.; Wu, G. X.; Meng, Q. C. Interactions of fully nonlinear solitary wave with a freely floating vertical cylinder. (English) Zbl 1403.76130 Eng. Anal. Bound. Elem. 69, 119-131 (2016). MSC: 76M15 65N38 76D33 PDFBibTeX XMLCite \textit{B. Z. Zhou} et al., Eng. Anal. Bound. Elem. 69, 119--131 (2016; Zbl 1403.76130) Full Text: DOI Link
Ducrozet, Guillaume; Bonnefoy, Félicien; Le Touzé, David; Ferrant, Pierre HOS-ocean: open-source solver for nonlinear waves in open ocean based on high-order spectral method. (English) Zbl 1380.65469 Comput. Phys. Commun. 203, 245-254 (2016). MSC: 65Y15 65M70 86A05 86-04 PDFBibTeX XMLCite \textit{G. Ducrozet} et al., Comput. Phys. Commun. 203, 245--254 (2016; Zbl 1380.65469) Full Text: DOI HAL
Bigoni, Daniele; Engsig-Karup, Allan P.; Eskilsson, Claes Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs. (English) Zbl 1360.76047 J. Eng. Math. 101, 87-113 (2016). MSC: 76B15 76M28 65M75 PDFBibTeX XMLCite \textit{D. Bigoni} et al., J. Eng. Math. 101, 87--113 (2016; Zbl 1360.76047) Full Text: DOI arXiv
Yan, Jinliang; Zhang, Qian; Zhang, Zhiyue New conservative finite volume element schemes for the modified Korteweg-de Vries equation. (English) Zbl 1359.65169 Math. Methods Appl. Sci. 39, No. 18, 5149-5161 (2016). Reviewer: Temur A. Jangveladze (Tbilisi) MSC: 65M08 65M60 35Q53 65M12 PDFBibTeX XMLCite \textit{J. Yan} et al., Math. Methods Appl. Sci. 39, No. 18, 5149--5161 (2016; Zbl 1359.65169) Full Text: DOI
Dutykh, Denys; Chhay, Marx; Clamond, Didier Numerical study of the generalised Klein-Gordon equations. (English) Zbl 1364.76028 Physica D 304-305, 23-33 (2015). MSC: 76B15 65M70 37K05 PDFBibTeX XMLCite \textit{D. Dutykh} et al., Physica D 304--305, 23--33 (2015; Zbl 1364.76028) Full Text: DOI arXiv
Wang, Jinghua; Ma, Q. W. Numerical techniques on improving computational efficiency of spectral boundary integral method. (English) Zbl 1352.76081 Int. J. Numer. Methods Eng. 102, No. 10, 1638-1669 (2015). MSC: 76M15 76B10 76M22 65M38 65M70 PDFBibTeX XMLCite \textit{J. Wang} and \textit{Q. W. Ma}, Int. J. Numer. Methods Eng. 102, No. 10, 1638--1669 (2015; Zbl 1352.76081) Full Text: DOI Link
Lannes, D.; Marche, F. A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations. (English) Zbl 1351.76114 J. Comput. Phys. 282, 238-268 (2015). MSC: 76M12 76M20 65M08 65M06 86A05 PDFBibTeX XMLCite \textit{D. Lannes} and \textit{F. Marche}, J. Comput. Phys. 282, 238--268 (2015; Zbl 1351.76114) Full Text: DOI
Popinet, Stéphane A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations. (English) Zbl 1349.76377 J. Comput. Phys. 302, 336-358 (2015). MSC: 76M12 65M08 65M55 76B15 PDFBibTeX XMLCite \textit{S. Popinet}, J. Comput. Phys. 302, 336--358 (2015; Zbl 1349.76377) Full Text: DOI
Gorban, I. M. A numerical study of solitary wave interactions with a bottom step. (English) Zbl 1335.76023 Sadovnichiy, Viktor A. (ed.) et al., Continuous and distributed systems II. Theory and applications. Cham: Springer (ISBN 978-3-319-19074-7/hbk; 978-3-319-19075-4/ebook). Studies in Systems, Decision and Control 30, 369-387 (2015). MSC: 76D33 35C08 35Q30 65N38 PDFBibTeX XMLCite \textit{I. M. Gorban}, Stud. Syst. Decis. Control 30, 369--387 (2015; Zbl 1335.76023) Full Text: DOI
Ducrozet, Guillaume; Engsig-Karup, Allan P.; Bingham, Harry B.; Ferrant, Pierre A non-linear wave decomposition model for efficient wave-structure interaction. part A: formulation, validations and analysis. (English) Zbl 1349.74358 J. Comput. Phys. 257, Part A, 863-883 (2014). MSC: 74S20 76M20 65M06 74J30 76B15 PDFBibTeX XMLCite \textit{G. Ducrozet} et al., J. Comput. Phys. 257, Part A, 863--883 (2014; Zbl 1349.74358) Full Text: DOI
Mitsotakis, Dimitrios; Ilan, Boaz; Dutykh, Denys On the Galerkin/finite-element method for the Serre equations. (English) Zbl 1299.76026 J. Sci. Comput. 61, No. 1, 166-195 (2014). MSC: 76B15 76B25 65M30 PDFBibTeX XMLCite \textit{D. Mitsotakis} et al., J. Sci. Comput. 61, No. 1, 166--195 (2014; Zbl 1299.76026) Full Text: DOI arXiv
Clamond, Didier; Dutykh, Denys Fast accurate computation of the fully nonlinear solitary surface gravity waves. (English) Zbl 1290.76018 Comput. Fluids 84, 35-38 (2013). MSC: 76B25 76M25 65T50 PDFBibTeX XMLCite \textit{D. Clamond} and \textit{D. Dutykh}, Comput. Fluids 84, 35--38 (2013; Zbl 1290.76018) Full Text: DOI arXiv
Dutykh, Denys; Clamond, Didier; Milewski, Paul; Mitsotakis, Dimitrios Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. (English) Zbl 1400.65053 Eur. J. Appl. Math. 24, No. 5, 761-787 (2013). MSC: 65M70 35Q35 65M08 76B25 PDFBibTeX XMLCite \textit{D. Dutykh} et al., Eur. J. Appl. Math. 24, No. 5, 761--787 (2013; Zbl 1400.65053) Full Text: DOI arXiv
Chhay, M.; Hoarau, E.; Hamdouni, A.; Sagaut, P. Comparison of some Lie-symmetry-based integrators. (English) Zbl 1416.65398 J. Comput. Phys. 230, No. 5, 2174-2188 (2011). MSC: 65M99 35A30 35Q53 PDFBibTeX XMLCite \textit{M. Chhay} et al., J. Comput. Phys. 230, No. 5, 2174--2188 (2011; Zbl 1416.65398) Full Text: DOI
Tsabary, Guy; Agnon, Yehuda Wave scattering from a rough surface: solution by an iterative method. (English) Zbl 1231.74231 Wave Motion 44, No. 7-8, 626-648 (2007). MSC: 74J20 76Q05 78A25 35J05 65T50 35P25 65N99 PDFBibTeX XMLCite \textit{G. Tsabary} and \textit{Y. Agnon}, Wave Motion 44, No. 7--8, 626--648 (2007; Zbl 1231.74231) Full Text: DOI
Fructus, Dorian; Clamond, Didier; Grue, John; Kristiansen, Øyvind An efficient model for three-dimensional surface wave simulations. I: Free space problems. (English) Zbl 1087.76016 J. Comput. Phys. 205, No. 2, 665-685 (2005). MSC: 76B15 65M70 76M25 PDFBibTeX XMLCite \textit{D. Fructus} et al., J. Comput. Phys. 205, No. 2, 665--685 (2005; Zbl 1087.76016) Full Text: DOI