A finite volume method parallelization for the simulation of free surface shallow water flows

Mathematics and Computers in Simulation

Volumn 79, Issue 11, 2009, Pages 3339-3359

  Delis, A I ^a   Mathioudakis, E N ^a  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

Distributed memory parallel architectures; Domain decomposition; Finite volume; Grid computing; Shallow water equations

Indexed keywords

APPROXIMATE RIEMANN SOLVER; BENCHMARK TESTS; DISTRIBUTED MEMORY ARCHITECTURE; DISTRIBUTED MEMORY PARALLEL ARCHITECTURES; DISTRIBUTED SHARED MEMORY; DOMAIN DECOMPOSITION; DOMAIN DECOMPOSITION TECHNIQUES; EXECUTION TIME; FINITE VOLUME; FREE SURFACES; PARALLEL CODE; PARALLELIZATION; SECOND ORDERS; SHALLOW WATER EQUATIONS; SHALLOW WATER FLOW; SHOCK-CAPTURING; SPATIAL ACCURACY; SPEED-UP FACTORS; TWO-DIMENSIONAL SHALLOW WATER EQUATIONS;

DOMAIN DECOMPOSITION METHODS; FINITE VOLUME METHOD; FLOW OF WATER; GRID COMPUTING; PARALLEL ALGORITHMS; SUPERCOMPUTERS; TWO DIMENSIONAL;

PARALLEL ARCHITECTURES;

EID: 67649435867     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2009.05.010     Document Type: Article

References (38)

1. Berman F., Fox G., and Hey A. Grid Computing: Making the Global Infrastructure a Reality (2003), Wiley
2. Bermudez A., and Vázquez-Cendón M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 (1994) 1049
3. Brufau P., and García-Navarro P. Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique. J. Comput. Phys. 186 (2003) 503
4. Burguete J., and García-Navarro P. Implicit schemes with large time step for non-linear equations: application to river flow hydraulics. Int. J. Numer. Methods Fluids 46 (2004) 607
5. Castro M.J., Garcia-Rodriguez J.A., Gonzalez-Vida J.M., and Pares C. A parallel 2D finite volume scheme for solving systems of balance laws with nonconservative products: application to shallow flows. Comput. Methods Appl. Mech. Eng. 195 (2006) 2788
6. Delis A.I. Higher order numerical methods evaluation for the computation of one-dimensional free surface shallow water flows. Int. J. Comput. Eng. Sci. 3 (2002) 13
7. Delis A.I., and Katsaounis Th. Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods. Appl. Math. Model. 29 (2005) 754
8. Delis A.I., Kazolea M., and Kampanis N.A. A robust high resolution finite volume scheme for the simulation of long waves over complex domain. Int. J. Numer. Methods Fluids 56 (2008) 419
9. Delis A.I., and Skeels C.P. TVD schemes for open channel flow. Int. J. Numer. Methods Fluids 26 (1998) 791
10. Delis A.I., Skeels C.P., and Ryrie S.C. Implicit high-resolution methods for modeling one-dimensional open channel flows. J. Hydraul. Res. 38 (2000) 369
11. Dongarra J., Foster I., Gropp W., Kennedy K., Toczon L., and White A. SourceBook of Parallel Computing (2003), Morgan Kaufmann
12. Ecer A., Akay H.U., Kemle W.B., Wang H., and Ercoskun D. Parallel computation of fluid dynamics problems. Comput. Methods Appl. Mech. Eng. 174 (1999) 433
13. 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. Methods Fluids 40 (2002) 1237
14. Fennema R.J., and Chaudhry M.H. Explicit methods for 2d transient free surface flows. J. Hydraul. Eng. ASCE 116 (1990) 1013
15. Foster I., and Kesselman C. The Grid 2: Blueprint for a New Computing Infrastructure (2004), Elsevier
16. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 1
17. Hubbard M.E., and Dodd N. A 2D numerical model of wave runup and overtoping. Coast. Eng. 47 (2002) 1
18. Hubbard M.E., and Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 165 (2000) 2
19. Hunter N.M., Bates P.D., Neelz S., Pender G., Villanueva I., Wright N.G., Liang D., Falconer R.A., Lin B., Waller S., Crossley A.J., and Mason D.C. Benchmarking 2D hydraulic models for urban flood simulations. Proc. Inst. Civ. Eng. Water Mgmt. 161 (2008) 13
20. Kramer S.C., and Stelling G.S. A conservative unstructured scheme for rapidly varied flows. Int. J. Numer. Methods Fluids 58 (2008) 183
21. LeVeque R.J. Balancing source terms and flux gradients in high-resolution Godunov type method: the quasi-steady wave propagation algorithm. J. Comput. Phys. 146 (1998) 346
22. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems (2002), Cambridge University Press
23. Manzini G., and Stolcis L. Distributed parallel strategies for industrial CFD solvers: a case study and analysis of performances. J. Parallel Distrib. Comput. 57 (1999) 334
24. Mathioudakis E., and Papadopoulou E. Grid computing for the Bi-CGSTAB applied to the solution of the modified Helmholtz equation. IJAMCS 4 (2007) 179
25. Mathioudakis E., Papadopoulou E., and Saridakis Y. Mapping parallel iterative algorithms for PDE computations on distributed memory computers. Parallel Algorithms Appl. 8 (1996) 141
26. Mathioudakis E., Papadopoulou E., and Saridakis Y. Bi-CGSTAB for collocation equations on distributed memory parallel computers. Num. Math. Adv. Appl. ENUMATH 1 (2003) 957
27. Mathioudakis E., Papadopoulou E., and Saridakis Y. Iterative solution of elliptic collocation systems on a cognitive parallel computer. Comput. Math. Appl. 48 (2004) 951
28. Message Passing Interface (MPI) http://www.mpi-forum.org.
29. Murillo J., Brufau P., and Garcia-Navarro P. Extension of an explicit finite volume method to large time steps (CFL > 1): application to shallow water flows. Int. J. Numer. Methods Fluids 50 (2006) 63
30. Rao P. A parallel hydrodynamic model for shallow water equations. Appl. Math. Comput. 150 (2004) 291
31. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357
32. SGI Origin 350 server http://www.sgi.com/products/remarketed/origin350.
33. SUN V240z server http://www.sun.com/servers/entry/v240.
34. Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 (1984) 995
35. Toro E.F. Shock-capturing Methods for Free-surface Shallow Flows (2001), Wiley
36. Toro E.F., and Garcia-Navarro P. Godunov-type methods for free-surface shallow flows: a review. J. Hydraul. Res. 45 (2007) 736
37. Vázquez-Cendón M.E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys. 148 (1999) 497
38. Ying X., Khan A.A., and Wang S.S.Y. An upwind conservative scheme for Saint Venant equations. J. Hydraul. Eng. ASCE 130 (2004) 977