A Modified Galerkin / Finite Element Method for the numerical solution of the Serre-Green-Naghdi system
作者： Mark Mcguinness , Costas Synolakis , Dimitrios Mitsotakis
DOI: 10.1002/FLD.4293
关键词: Boundary knot method 、 Mixed finite element method 、 Numerical stability 、 Discontinuous Galerkin method 、 Finite element method 、 Mathematical analysis 、 Numerical partial differential equations 、 Smoothed finite element method 、 Mathematics 、 Extended finite element method
摘要: A new modified Galerkin / Finite Element Method is proposed for the numerical solution of fully nonlinear shallow water wave equations. The method allows use low-order Lagrange finite element spaces, despite fact that system contains third order spatial partial derivatives depth averaged velocity fluid. After studying efficacy and conservation properties method, we proceed with validation model boundary conditions by comparing solutions laboratory experiments available theoretical asymptotic results.
arxiv.org
sci-hub.st 参考文章(59)
Eric Barth�lemy, Nonlinear Shallow Water Theories for Coastal Waves Surveys in Geophysics. ,vol. 25, pp. 315- 337 ,(2004) , 10.1007/S10712-003-1281-7
D.E. Mitsotakis, Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves Mathematics and Computers in Simulation. ,vol. 80, pp. 860- 873 ,(2009) , 10.1016/J.MATCOM.2009.08.029
Costas Emmanuel Synolakis, James Eric Skjelbreia, EVOLUTION OF MAXIMUM AMPLITUDE OF SOLITARY WAVES ON PLANE BEACHES Journal of Waterway Port Coastal and Ocean Engineering-asce. ,vol. 119, pp. 323- 342 ,(1993) , 10.1061/(ASCE)0733-950X(1993)119:3(323)
D. H. Peregrine, Long waves on a beach Journal of Fluid Mechanics. ,vol. 27, pp. 815- 827 ,(1967) , 10.1017/S0022112067002605
Maojun Li, Philippe Guyenne, Fengyan Li, Liwei Xu, High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model Journal of Computational Physics. ,vol. 257, pp. 169- 192 ,(2014) , 10.1016/J.JCP.2013.09.050
A.G. Filippini, S. Bellec, M. Colin, M. Ricchiuto, On the nonlinear behaviour of Boussinesq type models: Amplitude-velocity vs amplitude-flux forms Coastal Engineering. ,vol. 99, pp. 109- 123 ,(2015) , 10.1016/J.COASTALENG.2015.02.003
E. Peilnovsky, E. Troshina, V. Golinko, N. Osipenko, N. Petrukhin, Runup of tsunami waves on a vertical wall in a basin of complex topography Physics and Chemistry of The Earth Part B-hydrology Oceans and Atmosphere. ,vol. 24, pp. 431- 436 ,(1999) , 10.1016/S1464-1909(99)00024-6
Okey Nwogu, Alternative form of Boussinesq equations for nearshore wave propagation Journal of Waterway Port Coastal and Ocean Engineering-asce. ,vol. 119, pp. 618- 638 ,(1993) , 10.1061/(ASCE)0733-950X(1993)119:6(618)
Boaz Ilan, Denys Dutykh, Dimitrios Mitsotakis, On the Galerkin/Finite-Element Method for the Serre Equations Journal of Scientific Computing. ,vol. 61, pp. 166- 195 ,(2014) , 10.1007/S10915-014-9823-3
D. C. Antonopoulos, V. A. Dougalis, Error estimates for Galerkin approximations of the “classical” Boussinesq system Mathematics of Computation. ,vol. 82, pp. 689- 717 ,(2012) , 10.1090/S0025-5718-2012-02663-9