Space discontinuous Galerkin method for shallow water flows-kinetic and HLLC flux, and potential vorticity generation

Advances in Water Resources

Volumn 30, Issue 4, 2007, Pages 998-1015

  Tassi, P A ^a,b   Bokhove, O ^a   Vionnet, C A ^b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b UNIVERSIDAD NACIONAL DEL LITORAL   (Argentina)

Author keywords

Bore vortex interactions; Discontinuity detector; Discontinuous Galerkin; Finite elements; Potential vorticity generation; Shallow water flows

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FLOW INTERACTIONS; GALERKIN METHODS; HYDRAULIC JUMP; MATHEMATICAL MODELS; VORTICITY;

BORE-VORTEX INTERACTION; POTENTIAL VORTICITY GENERATION; SHALLOW WATER FLOWS;

FLOW OF WATER;

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FLOW INTERACTIONS; FLOW OF WATER; GALERKIN METHODS; HYDRAULIC JUMP; MATHEMATICAL MODELS; VORTICITY;

BOTTOM TOPOGRAPHY; FINITE ELEMENT METHOD; GALERKIN METHOD; HYDRAULICS; NUMERICAL MODEL; POTENTIAL VORTICITY; SHALLOW WATER; VORTEX FLOW; WATER FLOW;

EID: 33847055400     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2006.09.003     Document Type: Article

References (42)

1. Akers B. Shallow water flow through a contraction. http://gfd.whoi.edu/proceedings/2005/PDFvol2005.html; 2005.
2. Al-Tarazi M, Bokhove O, Kuipers J, Van Sint Annaland M, Vreman AW. Reservoir formation in shallow granular flows through a contraction. http://eprints.eemcs.utwente.nl/; 2005.
3. Ambati VR, Bokhove O. Space-time discontinuous Galerkin finite element modeling of rotating shallow water flows. J Comput Phys, submitted for publication. http://eprints.eemcs.utwente.nl/; 2006.
4. Atkinson P.H., Westerink J.J., and Hervouet J.-M. Similarities between the quasi-bubble and the generalized wave continuity equation solutions to the shallow water equations. Int J Numer Methods Fluids 45 (2004) 689-714
5. Batten P., Clarke N., Lambert C., and Causon D.M. On the choice of wavespeeds for the HLLC Riemann solver. SIAM J Sci Comput 18 6 (1997) 1552-1570
6. Bokhove O. Flooding and drying in finite-element Galerkin discretizations of shallow-water equations. Part I: One dimension. J Sci Comput 22 (2005) 47-82
7. Bokhove O. Hamiltonian restriction of Vlasov equations into two-layer isopycnic and isentropic equations. Appl Math Lett 18 (2005) 1418-1425
8. Bokhove O., Woods A.W., and Boer de A. Magma flow through elastic-walled dikes. Theor Comput Fluid Dyn 19 (2005) 261-286
9. Audusse E., Bouchut F., Bristeau M.-O., Klein R., and Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J Sci Comput 25 (2004) 2050-2065
10. Bühler O. On the vorticity transport due to dissipating or breaking waves in shallow-water flow. J Fluid Mech 407 (2000) 235-263
11. Castro M., Gallardo J.M., and Pares C. High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. Math Comput 75 (2006) 1103-1134
12. Chippada S., Dawson C.N., Martinez M.L., and Wheeler M.F.A. Godunov-type finite volume method for the system of shallow water equations. Comput Methods Appl Mech Eng 151 (1998) 105-129
13. Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin finite element method for conservation laws V: Multidimensional systems. J Comput Phys 141 (1998) 199-224
14. Cockburn B. Discontinuous Galerkin methods for convection-dominated problems. In: Timothy Barth J, Herman Deconinck, editors. High-order methods for computational physics, vol. 9, 1999. p. 69-224.
15. Cockburn B., Karniadakis G.E., and Shu C.-W. The development of discontinuous Galerkin methods. Discontinuous Galerkin methods: theory, computation and applications. In: Shu C.-W., Cockburn B., and Karniadakis G.E. (Eds). Lecture notes in computational science and engineering vol. 11 (2000), Springer, New York, Heidelberg
16. Flaherty J.E., Loy R.M., Shepard M.S., and Teresco J.D. Software for the parallel adaptive solution of conservation laws by discontinuous Galerkin methods. Discontinuous Galerkin methods: theory, computation and applications. In: Shu C.-W., Cockburn B., and Karniadakis G.E. (Eds). Lecture notes in computational science and engineering vol. 11 (2000), Springer, New York, Heidelberg
17. Hall P. Alternating bar instabilities in unsteady channel flows over erodible beds. J Fluid Mech 499 (2004) 49-73
18. Harten A., Lax P.D., and van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev 25 (1983) 35-61
19. Houghton D.D., and Kasahara A. Nonlinear shallow fluid flow over an isolated ridge. Commun Pure Appl Math 21 (1968) 1-23
20. Hu G. Note on numerical simulation of shallow water. Bristol University, School of Mathematics, Rep No AM-02-01, 2002. 17pp.
21. Jaffre J., Johnson C., and Szepessy A. Convergence of the discontinuous Galerkin finite element method for hyperbolic conservation laws. Math Models Methods Appl Sci 5 3 (1995) 367-386
22. Katopodes N.D. A dissipative Galerkin scheme for open-channel flows. J Hydraul Eng ASCE 110 (1984) 450-466
23. Krivodonova L., Xin J., Remacle J.-F., and Chevaugeon N. Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. Appl Numer Math 48 (2004) 323-338
24. Lamb J. Hydrodynamics (1993), Cambridge University Press
25. Leer van B. Towards the ultimate conservative difference scheme V: a second-order sequel to Godunov's method. J Comput Phys 32 (1979) 361-370
26. LeVeque RJ. Numerical methods for conservation laws. Lectures in mathematics ETH Zürich; 1990.
27. Matsutomi H., and Mochizula A. Behaviour of a bore over a conical shoal. Tohoku J Nat Disaster Sci (2001) [in Japanese]
28. Morrison P.J. The Maxwell-Vlasov equations as a continuous hamiltonian system. Phys Lett 80 (1980) 383-386
29. Pedlosky J. Geophysical fluid dynamics. 2nd ed. (1987), Springer
30. Peregrine D.H. Surf zone currents. Theor Comput Fluid Dyn 10 (1998) 295-310
31. Peregrine D.H. Large-scale vorticity generation in breakers in shallow and deep water. J Mech B/Fluids 18 (1999) 403-408
32. Perthame B. An introduction to kinetic schemes for gas dynamics. In: Rohde C., Kröner D., and Ohlberger M. (Eds). An introduction to recent developments in theory and numerics for conservation laws (1999), Springer-Verlag 1-27
33. Perthame B., and Simeoni C. A kinetic scheme for the Saint-Venant scheme with a source term. Calcolo 38 (2001) 201-231
34. Pratt L.J. On inertial flow over topography. Part 1. Semigeostrophic adjustment to an obstacle. J Fluid Mech 131 (1983) 195-218
35. Shu C.-W. TVD time discretizations. SIAM J Sci Stat Comput 9 (1988) 1073-1084
36. Tassi P, Bokhove O, Vionnet C. Additional appendices, http://eprints.eemcs.utwente.nl/; 2006.
37. Toro E.F. Riemann solvers and numerical methods for fluid dynamics: a practical introduction (1997), Springer
38. Vegt van der J.J.W., and Vegt van der H. Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I: General formulation. J Comput Phys 182 (2002) 546-585
39. Vreugdenhil C.B. Numerical methods for shallow water flow. 2nd ed. (1994), Kluwer Academic Publishers., Dordrecht, Netherlands
40. Walters R.A., and Carey G.F. Analysis of spurious oscillations modes for the shallow-water and Navier-Stokes equations. Comput Fluids 11 2 (1983) 51-68
41. Whitham G.B. Linear and nonlinear waves (1974), John Wiley, London
42. Zienkiewics O.C., and Ortiz P. A split-characteristic based finite element model for the shallow water equations. Int J Numer Methods Fluids 20 2 (1995) 1061-1080