Simulation of hydraulic shock waves by hybrid flux-splitting schemes in finite volume method

Journal of Mechanics

Volumn 21, Issue 2, 2005, Pages 85-101

  Lai, J S ^a   Lin, G F ^b   Guo, W D ^b  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Flux difference splitting; Flux vector splitting; Hybrid flux splitting finite volume scheme; Shallow water flows

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; ENTROPY; FINITE VOLUME METHOD; HYDRAULICS; MATRIX ALGEBRA; REFRACTION; VECTORS;

FLUX-DIFFERENCE SPLITTING; FLUX-VECTOR SPLITTING; HYBRID FLUX-SPLITTING FINITE-VOLUME SCHEME; SHALLOW WATER FLOWS;

SHOCK WAVES;

EID: 20844462031     PISSN: 17277191     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1727719100004561     Document Type: Article

References (27)

1. Hirsch, C., Numerical Computation of Internal and External Flows, 2nd Edition, John Wiley & Sons, New York (1990).
2. Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin (1997).
3. Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," J. Comput. Phys., 43, pp. 357-372 (1981).
4. Steger, J. L. and Warming, R. F., "Flux Vector Splitting of the Inviscid Gas Dynamic Equations with Application to Finite Difference Methods," J. Comput. Phys., 40, pp. 263-293 (1981).
5. Osher, S. and Solomone, F., "Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws," Mathematics and Computers in Simulation, 38, pp. 339-374 (1982).
6. Nujic, M., "Efficient Implementation of Non-Oscillatory Schemes for the Computation of Free-Surface Flows," J. Hydraulic Res., 33(1), pp. 101-111 (1995).
7. Mingham, C. G. and Causon, D. M., "High-Resolution Finite-Volume Method for Shallow Water Flows," J. Hydraulic Eng., 124(6), pp. 605-614 (1998).
8. Hu, K., Mingham, C. G. and Causon, D. M., "A Bore-Capturing Finite Volume Method for Open-Channel Flows," Int. J. Numer. Meth. Fluids, 28, pp. 1241-1261 (1998).
9. Tseng, M. H., "Explicit Finite Volume Non-Oscillatory Schemes for 2D Transient Free-Surface-Flows," Int. J. Numer. Meth. Fluids, 30, pp. 831-843 (1999).
10. Tseng, M. H. and Chu, C. R., "Two-Dimensional Shallow Water Flows Simulation using TVD-MacCormack Scheme," J. Hydraulic Res., 38(2), pp. 123-131 (2000).
11. Lin, G. F., Lai, J. S. and Guo, W. D., "Finite-Volume Component-Wise TVD Schemes for 2D Shallow Water Equations," Adv. Water Resour., 26(8), pp. 861-873 (2003).
12. Erduran, K. S., Kutija, V. and Hewett, C. J. M., "Performance of Finite Volume Solutions to the Shallow Water Equations with Shock-Capturing Schemes," Int. J. Numer. Meth. Fluids, 40, pp. 1237-1273 (2002).
13. Liou, M. S. and Steffen, C. J., "A New Flux Splitting Scheme," J. Comput. Phys., 107, pp. 23-39 (1993).
14. Liou, M. S., "A Sequel to AUSM: AUSM+," J. Comput. Phys., 129, pp. 364-382 (1996).
15. Wada, Y. and Liou, M. S., "An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities," SIAM Journal of Scientific Computing, 18(3), pp. 633-657 (1997).
16. Niu, Y. Y., "Advection Upstream Splitting Method to Solve a Compressible Two-Fluid Model," Int. J. Numer. Meth. Fluids, 36, pp. 351-371 (2001).
17. Evje, S. and Fjelde, K. K., "Hybrid Flux-Splitting Schemes for a Two-Phase Flow Model," J. Comput. Phys., 175, pp. 674-701 (2002).
18. Hus, U. K., Tai, C. H. and Tsa, C. H., "All Speed and High-Resolution Scheme Applied to Three-Dimensional Multi-Block Complex Flow Field System," Journal of Mechanics, 20(1), pp. 13-25 (2004).
19. Tan, W. Y., Shallow Water Hydrodynamics, Elsevier, New York (1992).
20. Toro, E. F., Shock-Capturing Methods for Free-Surface Shallow Water Flows, John Wiley & Sons, New York (2001).
21. Bellos, C. V., Soulis, J. V. and Sakkas, J. G., "Experimental Investigation of Two-Dimensional Dam-Break Induced Flows," J. Hydraulic Res., 30(1), pp. 47-63 (1992).
22. Stoker, J. J., Water Waves: Mathematical Theory with Applications, Wiley-Interscience, Singapore (1958).
23. Harten, A. and Hyman, J. M., "Self Adjusting Grid Methods for ID Hyperbolic Conservation Laws," J. Comput. Phys., 50, pp. 235-269 (1983).
24. LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, U.K. (2002).
25. Alcrudo, F. and Garcia-Navarro, P., "A High-Resolution Godunove-Type Scheme in Finite Volumes for the 2D Shallow Water Equations," Int. J. Numer. Meth. Fluids, 16, pp. 489-505 (1993).
26. Brufau, P. and Garcia-Navarro, P., "Two-Dimensional Dam Break Flow Simulation," Int. J. Numer. Meth. Fluids, 33, pp. 35-57 (2000).
27. Hager, W. H., Schwalt, M., Jimenez, O. and Chaudry, M. H., "Supercritical Flow near an Abrupt Wall Deflection," J. Hydraulic Res., 32(1), pp. 103-118 (1994).