Finite element approximation of the modified Boussinesq equations using a stabilized formulation

International Journal for Numerical Methods in Fluids

Volumn 57, Issue 9, 2008, Pages 1249-1268

  Codina, Ramon ^a   González Ondina, José M ^b   Díaz Hernández, Gabriel ^b   Principe, Javier ^a  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

^b ENVIRONMENTAL HYDRAULICS INSTITUTE IH CANTABRIA   (Spain)

Author keywords

Boussinesq equations; Mixed interpolations; Non linear waves; Stabilized finite elements

Indexed keywords

MATHEMATICAL MODELS;

BOUSSINESQ EQUATIONS; FINITE ELEMENT; FINITE ELEMENT APPROXIMATIONS; FINITE ELEMENT MODEL; HIGH-ORDER DERIVATIVES; MIXED INTERPOLATIONS; NON-LINEAR WAVES; STABILIZATION TECHNIQUES; STABILIZED FINITE ELEMENTS; STABILIZED FORMULATION; SUB-GRID SCALE; SYSTEM OF EQUATIONS; TIME-INTEGRATION SCHEMES;

FINITE ELEMENT METHOD;

EID: 48549086035     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1718     Document Type: Conference Paper

References (22)

1. Nwogu O. Alternative form of Boussinesq equations for near shore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering (ASCE) 1993; 119:618-638.
2. Hughes TJR. Multiscale phenomena: Green's function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations. Computer Methods in Applied Mechanics and Engineering 1995; 127:387-401.
3. Hughes TJR, Feijóo GR, Mazzei L, Quincy JB. The variational multiscale method - a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering 1998; 166:3-24.
4. Codina R. Finite element approximation of the hyperbolic wave equation in mixed form. Computer Methods in Applied Mechanics and Engineering 2007; DOI: 10.1016/j.cma.2007.11.006.
5. Abbot MB, Petersen HM, Skovgaard O. On the numerical modelling of short waves in shallow water. Journal of Hydraulic Research 1978; 16:173-203.
6. Wei G, Kirby JT. Time dependent numerical code for extended Boussinesq equations. Journal of Waterway, Port, Coastal and Ocean Engineering (ASCE) 1995; 121:251-261.
7. Langtangen HP, Pedersen G. Computational models for weakly dispersive nonlinear water waves. Computer Methods in Applied Mechanics and Engineering 1998; 160:337-358.
8. Li YS, Liu S-X, Yu Y-X, Lai G-Z. Numerical modeling of the Boussinesq equations by finite element method. Coastal Engineering 1999; 37:97-122.
9. Walkley M, Berzins M. A finite element method for the two-dimensional extended Boussinesq equations. International Journal for Numerical Methods in Fluids 2002; 39:865-885.
10. Woo S-B, Liu PL-F. Finite element model for modified Boussinesq equations. I: model development. Journal of Waterway, Port, Coastal and Ocean Engineering (ASCE) 2004; 130:1-16.
11. Donea J. A Taylor-Galerkin method for convection transport problems. International Journal for Numerical Methods in Engineering 1984; 20:101-119.
12. Peraire J, Zienkiewicz OC, Morgan K. Shallow water problems: a general explicit formulation. International Journal for Numerical Methods in Engineering 1986; 22:547-574.
13. Miglio E, Quarteroni A, Saleri F. Finite element approximation of quasi-3d shallow water equations. Computer Methods in Applied Mechanics and Engineering 1999; 174:355-369.
14. Zienkiewicz OC, Ortiz P. A split-characteristic based finite element model for the shallow water equations. International Journal for Numerical Methods in Fluids 1995; 20:1061-1080.
15. Hauke G. A symmetric formulation for computing transient shallow water flows. Computer Methods in Applied Mechanics and Engineering 1998; 163:111-122.
16. Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Computer Methods in Applied Mechanics and Engineering 2002; 191:4295-4321.
17. Israeli M, Orzag SA. Approximation of radiation boundary conditions. Journal of Computational Physics 1981; 42:115-135.
18. Berenger JP. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 1994; 114:185-200.
19. Codina R, Principe J, Guasch O, Badia S. Time dependent subscales in the stabilized finite element approximation of incompressible flow problems. Computer Methods in Applied Mechanics and Engineering 2007; 196: 2413-2430.
20. Codina R, Principe J. Dynamic subscales in the finite element approximation of thermally coupled incompressible flows. International Journal for Numerical Methods in Fluids 2007; 54:707-730.
21. Woo S-B, Liu PL-F. Finite element model for modified Boussinesq equations. II: application to nonlinear harbor oscillations. Journal of Waterway, Port, Coastal and Ocean Engineering (ASCE) 2004; 130:17-28.
22. Losada IJ, González-Ondina JM, Díaz-Hernandez G, González EM. Numerical modeling of nonlinear resonance of semi-enclosed water bodies: description and experimental validation. Coastal Engineering 2008; 55:21-34.