A robust high-resolution finite volume scheme for the simulation of long waves over complex domains

International Journal for Numerical Methods in Fluids

Volumn 56, Issue 4, 2008, Pages 419-452

  Delis, A I ^a,b   Kazolea, M ^a,b   Kampanis, N A ^b  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

^b INSTITUTE OF COMPUTER SCIENCE   (Greece)

Author keywords

Finite volume; Long waves; Shallow water equations; Wave breaking; Wave runup and rundown; Wet dry fronts

Indexed keywords

COMPUTER SIMULATION; FINITE VOLUME METHOD; HYDRAULIC JUMP; SURFACE WAVES;

BREAKING WAVE; FLOW DISCONTINUITY; RIEMANN SOLVER; SHALLOW WATER EQUATION;

WATER WAVES;

COMPUTER SIMULATION; FINITE VOLUME METHOD; HYDRAULIC JUMP; SURFACE WAVES; WATER WAVES;

EID: 38949188197     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1537     Document Type: Article

References (41)

1. Carrier GF, Greenspan HP. Water waves of finite amplitude on a sloaping beach. Journal of Fluid Mechanics 1958; 4:97-109.
2. Thacker WC. Some exact solutions to the nonlinear shallow water wave equations. Journal of Fluid Mechanics 1981; 107:499-508.
3. Synolakis CE. The run up of solitary waves. Journal of Fluid Mechanics 1987; 185:523-545.
4. Liu PL-F, Lynett P, Synolakis CE. Analytical solutions for forced long waves on a sloping beach. Journal of Fluid Mechanics 2003; 478:101-109.
5. Carrier GF, Wu TT, Yeh H. Tsunami run-up and draw-down on a plane beach. Journal of Fluid Mechanics 2003; 475:79-99.
6. Titov VV, Synolakis CE. Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2. Journal of Waterway, Port, Coastal and Ocean Engineering 1995; 121:308-461.
7. Liu PL-F, Cho Y-S, Griggs MJ, Kanoglou U, Synolakis CE. Runup of solitary wave on a circular island. Journal of Fluid Mechanics 1995; 302:259-285.
8. Titov VV, Synolakis CE. Numerical modeling of tidal wave runup. Journal of Waterway, Port, Coastal and Ocean Engineering 1998; 124:157-171.
9. Li Y, Raichlen F. Non-breaking and breaking solitary wave run-up. Journal of Fluid Mechanics 2002; 456:295-318.
10. Dodd N. Numerical model of wave run-up, overtopping and regeneration. Journal of Waterway, Port, Coastal and Ocean Engineering 1998; 124:73-81.
11. Hubbard ME, Dodd N. A 2D numerical model of wave runup and overtopping. Coastal Engineering 2002; 47:1-26.
12. Lynett PJ, Wu TR, Liu PL. Modeling wave runup with depth integrated equations. Coastal Engineering 2002; 46:89-107.
13. Hu K, Mingham CG, Causon DM. Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations. Coastal Engineering 2000; 41:433-465.
14. LeVeque RJ, George DL. High-resolution finite volume methods for the shallow water equations with bathymetry and dry states. In Advanced Numerical Models for Simulating Tsunami Waves and Runup, Yeh H, Liu PL, Synolakis CE (eds). Advances in Coastal and Ocean Engineering, vol. 10. World Scientific Publishing Co.: Singapore, in press.
15. Mader CL. Numerical Modeling of Water Waves. CRC Press: Boca Raton, 2004.
16. Imamura F. Review of tsunami simulation with finite difference method. In Long-Wave Runup Models, Yeh H, Liu P, Synolakis RC (eds). World Scientific Publishing Co.: Singapore, 1996; 25-42.
17. Bradford SF, Sanders BF. Finite-volume model for shallow-water flooding of arbitary torography. Journal of Hydraulic Engineering 2002; 128:289-298.
18. Brocchini M, Bernetti R, Mancinelli A, Albertini G. An efficient solver for nearshore flows based on the WAF method. Coastal Engineering 2001; 43:105-129.
19. Gopalakrishnan TC, Tung CC. Run-up of non-breaking waves: a finite-element approach. Coastal Engineering 1980; 4:3-32.
20. Zelt JA. The run-up of nonbreaking and breaking solitary waves. Coastal Engineering 1991; 15:205-246.
21. Yeh H, Liu PL, Synolakis CE (eds). Long Wave Runup Models. World Scientific Publishing Co.: Singapore, 1996.
22. Helluy P, Golay F, Caltagirone J-P, Lubin P, Vincent S, Drevard D, Marcer R, Fraunie P, Seguin N, Grilli S, Lesage A-C, Dervieux A, Allain O. Numerical simulations of wave breaking. ESAIM: Mathematical Modelling and Numerical Analysis 2005; 39(3):591-607.
23. Vincent S, Caltagirone JP, Bonneton P. Numerical modelling of bore propagation and runup on sloping braches using a MacCormack TVD scheme. Journal of Hydraulic Research 2001; 39:41-49.
24. Cea L, Ferreiro A, Vázquez-Cendnó ME, Puertas J. Experimental and numerical analysis of solitary waves generated by bed and boundary movements. International Journal for Numerical Methods in Fluids 2004; 46:793-813.
25. Marche F, Bonneton P, Fabrie P, Seguin N. Evaluation of well-balanced bore-capturing schemes for 2d wetting and drying processes. International Journal for Numerical Methods in Fluids 2007; 53:867-894.
26. Roe PL. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics 1981; 43:357-372.
27. Bermudez A, Vázquez-Cendón ME. Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids 1994; 23:1049-1071.
28. Vázquez-Cendón ME. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. Journal of Computational Physics 1999; 148:497-526.
29. LeVeque RJ. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press: Cambridge, 2002.
30. Harten A. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics 1983; 49:357-393.
31. Delis AI, Skeels CP. TVD schemes for open channel flow. International Journal for Numerical Methods in Fluids 1998; 26:791-809.
32. Brufau P, García-Navarro P, Vázquez-Cendón ME. Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography. International Journal for Numerical Methods in Fluids 2004; 45:1047-1082.
33. Castro MJ, Ferreiro AM, García-Rodriguez JA, González-Vida JM, Macías J, Parés C, Vázquez-Cendón ME. The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. Mathematical and Computer Modelling 2005; 42:419-439.
34. Brufau P, Vázquez-Cendón ME, Gracía-Navarro P. A numerical model for the flooding and drying of irregular domain. International Journal for Numerical Methods in Fluids 2002; 39:247-275.
35. Castro MJ, González-Vida JM, Parés C. Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. Mathematical Models and Methods in Applied Sciences 2006; 16:897-931.
36. Hubbard ME, Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. Journal of Computational Physics 2000; 165:89-125.
37. Sweby PK. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis 1984; 21:995-1011.
38. Yeh H, Liu PL, Synolakis CE (eds). Advanced Numerical Models for Simulating Tsunami Waves and Runup, Advances in Coastal and Ocean Engineering, vol. 10. World Scientific Publishing Co.: Singapore, in press.
39. Cea L, French JR, Vázquez-Cendón ME. Numerical modelling of tital flows in complex estuaries including turbulance: an unstructured finite volume solver and experimental validation. International Journal for Numerical Methods in Engineering 2006; 67:1909-1932.
40. Brufau P, García-Navarro P. Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique. Journal of Computational Physics 2003; 186:503-526.
41. Delis AI, Katsaounis Th. Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods. Applied Mathematical Modelling 2005; 29:754-783.