A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations

International Journal for Numerical Methods in Fluids

Volumn 45, Issue 6, 2004, Pages 605-623

  Eskilsson, C ^a,b   Sherwin, Spencer J ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Discontinuous Galerkin method; Shallow water equations; Spectral hp discretization

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; GALERKIN METHODS; POLYNOMIALS; RUNGE KUTTA METHODS;

GIBBS OSCILLATIONS; NUMERICAL FLUXES; SHALLOW WATER FLOWS;

FLOW OF FLUIDS;

COMPUTATIONAL FLUID DYNAMICS; EQUATION; MATHEMATICAL ANALYSIS; SHALLOW WATER; TWO-DIMENSIONAL FLOW;

EID: 2942574229     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.709     Document Type: Article

References (24)

1. Abbott MB. Computational hydraulics. Elements of the Theory of Free Surface Flows. Pitman: London, 1979.
2. Chaudry MH. Open-Channel Flow. Pretice-Hall: New Jersey, 1993.
3. Toro EF. Shock-Capturing Methods for Free Surface Flows. Wiley: Chichester, 2001.
4. Ma H. A spectral element basin model for the shallow water equations. Journal of Computational Physics 1993; 109:133-149.
5. Iskandarani M, Haidvogel DB, Boyd JP. A staggered spectral element model with application to the oceanic shallow water equations. International Journal for Numerical Methods in Fluids 1995; 20:393-414.
6. Cockburn B, Lin S-Y, Shu C-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems. Journal of Computational Physics 1989; 84: 90-113.
7. Cockburn B, Shu C-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws V: multidimensional systems. Journal of Computational Physics 1998; 141:199-224.
8. Cockburn B, Shu C-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Journal of Scientific Computing 2001; 16(3):173-261.
9. Biswas R, Devine KD, Flaherty JE. Parallel, adaptive finite element methods for conservation laws. Applied Numerical Mathematics 1994; 14:255-283.
10. Burbeau P, Sagaut P, Bruneau Ch-H. A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods. Journal of Computational Physics 2001; 169:111-150.
11. Lomtev I. A discontinuous Galerkin spectral/hp element method for compressible Navier-Stokes equations. Ph.D. Thesis, Brown University, 1998.
12. Schwanenberg D, Köngeter J. A discontinuous Galerkin method for the shallow water equations with source terms. In Discontinuous Galerkin Methods, Cockburn B, Kamiadakis GE, Shu C-W (eds). Springer: Heidelberg, 2000; 289-309.
13. Li H, Liu RX. The discontinuous Galerkin finite element method for the 2d shallow water equations. Mathematics and Computers in Simulation 2001; 56:171-184.
14. Aizinger V, Dawson C. A discontinuous Galerkin method for two-dimensional flow and transport in shallow water. Advances in Water Resources 2002; 25:67-84.
15. Dupont, F. Comparison of numerical methods for modelling ocean circulation in basins with irregular coasts. Ph.D. Thesis, McGill University, 2001.
16. Giraldo FX, Hesthaven JS, Warburton T. Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations. Journal of Computational physics 2002; 181:499-525.
17. Proriol J. Sur une famille de polynomes á deux variables orthogonaux dans un triangle. Comptes Rendes de'l Academie des Sciences Paris 1957; 257:2459.
18. Koornwinder T. Two-variable analogues of the classical orthogonal polynomials. Theory and Applications of Special Functions. Academic Press: San Diego, 1975.
19. Dubiner M. Spectral methods on triangles and other domains. Journal of Scientific Computing 1991; 6(4):345-390.
20. Karniadakis EmG, Sherwin SJ. Spectral/hp Element Methods for CFD. Oxford University Press: US, 1999.
21. Sanders BF. Non-reflecting boundary flux function for finite volume shallow-water models. Advances in Water Resources 2002; 25:195-202.
22. Boyd JP. Equatorial solitary waves. Part I: Rossby solitons. Journal of Physical Oceanography 1980; 10:1699-1717.
23. Wang J-W, Liu R-X. A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems. Mathematics and Computers in Simulation 2000; 53:171-184.
24. Zoppou C, Roberts S. Numerical solution of the two-dimensional unsteady dam break. Applied Mathematical Modelling 2000; 24:457-475.