Hybrid finite element/volume method for shallow water equations

International Journal for Numerical Methods in Engineering

Volumn 83, Issue 13, 2010, Pages 1719-1738

  Aliabadi, Shahrouz ^a   Akbar, Muhammad ^a   Patel, Reena ^a  

^a Northrop Grumman Center for High Performance Computing ^*  (United States)

Author keywords

Finite element methods; Finite volume methods; Hybrid method; Shallow water equations; Shock capturing

Indexed keywords

ACCURATE CELLS; FINITE ELEMENT; FINITE VOLUME SCHEMES; GOVERNING EQUATIONS; HIGH REYNOLDS NUMBER FLOWS; HYBRID METHOD; ITERATIVE SOLVERS; LINEAR INTERPOLATION; MATRIX; MOMENTUM EQUATION; NONLINEAR WAVE EQUATION; NUMERICAL SCHEME; PRIMITIVE VARIABLES; SEGREGATED METHODS; SHALLOW WATER EQUATIONS; SHALLOW WATER FLOW; SHARP INTERFACE; SHOCK-CAPTURING; TEST PROBLEM; TWO-FLUID FLOW;

FINITE VOLUME METHOD; INCOMPRESSIBLE FLOW; NUMERICAL METHODS; REYNOLDS NUMBER; WAVE EQUATIONS;

FINITE ELEMENT METHOD;

EID: 77956841758     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2886     Document Type: Article

References (34)

1. Bermudez A, Vazquez ME. Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids 1994; 23(8):1049-1071.
2. LeVeque RJ. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press: Cambridge, 2002.
3. Bale D, LeVeque RJ, Mitran S, Rossmanith J. A wave-propagation method for conservation laws or balance laws with spatially varying flux functions. SIAM Journal on Scientific Computing 2002; 24:266-278.
4. Buffard T, Gallouët T, Hérard JM. A naive scheme to solve shallow-water equations. CRAS Paris I-326 1998; 385-390.
5. Gallouet T, Jean-Marc H. Some approximate Godunov schemes to compute shallow water equations with topography. Computers and Fluids 2003; 32:479-513.
6. Kurganov A, Levy D. Central upwind schemes for the St. Venant system. Mathematical Modeling and Numerical Analysis 2002; 36:397-425.
7. Botta N, Klein R, Langenberg S, Lutzenkirchen S. Well balanced finite volume methods for nearly hydrostatic flows. Journal of Computational Physics 2004; 196:539-565.
8. Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43:357-372.
9. Harten A, Lax PD, van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 1983; 25:235-261.
10. Sweby PK. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis 1984; 21:995.
11. Lynch DR, Gray WG. A wave equation model for finite element tidal computations. Computers and Fluids 1979; 7(3):207-228.
12. Kawahara M, Kashiyama K. Selective lumping finite element method for near shore current. International Journal for Numerical Methods in Fluids 1984; 4:71-97.
13. Kinnmark IPE. The Shallow Water Wave Equations: Formulations, Analysis, and Application. Lecture Notes in Engineering, vol. 15. Springer: Berlin, 1986.
14. Luettich RA, Westerink JJ, Scheffner NW. ADCIRC: An advanced three-dimensional circulation model for shelves, coasts and estuaries; Report 1: Theory and methodology of ADCIRC-2DDI and ADCIRC-3DL. Technical Report DRP-92-6, Department of the Army, USACE, Washington, DC, 1991.
15. Westerink JJ, Luettich RA, Blain CA, Scheffner NW. An Advanced Three-dimensional Circulation Model for Shelves, Coasts and Estuaries; Report 2: Users Manual for ADCIRC-2DDI, Deparment of the Army, USACE. Washington, DC, 1992.
16. Kolar RL, Gray WG, Westerink JJ, Luettich RA. Shallow water modeling in spherical coordinates: equation formulation, numerical implementation and application. Journal of Hydraulic Research 1994; 32(1):3-24.
17. Tu S, Aliabadi S. Development of a hybrid finite volume/element solver for incompressible flows. International Journal for Numerical Methods in Fluids 2007; 55:177-203.
18. Tu S, Aliabadi S, Patel R, Watts M. An implementation of the Spalart-Allmaras DES model in an implicit unstructured hybrid finite volume/element solver for incompressible turbulent Flow. International Journal for Numerical Methods in Fluids 2009; 59:1051-1062.
19. Wan T, Aliabadi S, Bigler C. A hybrid scheme based on finite element/volume methods for two immiscible fluid flows. International Journal for Numerical Methods in Fluids 2009; 61(8):930-944.
20. Wan T, Aliabadi S, Bigler C. A parallel hybrid finite element/volume methods for two immiscible fluid flows. 19th AIAA Computational Fluid Dynamics Conference, San Antonio, TX, 22-25 June 2009. AIAA Paper Number: 2009-3887.
21. Guermond JL, Minev P, Shen J. An overview of projection methods for incompressible fows. Computer Methods in Applied Mechanics and Engineering 2006; 195:6011-6045.
22. Timmermans LJP, Minev PD, van de Vosse FN. An approximate projection scheme for incompressible flow using spectral elements. International Journal for Numerical Methods in Fluids 1996; 22:673-688.
23. Aliabadi S, Johnson AA, Abedi J. Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces. Computer and Fluids 2003; 32:535-545.
24. Aliabadi S, Tu S, Watts MD, Ji A, Johnson AA. Integrated high performance computational tools for simulations of transport and diffusion of contaminants in urban areas. International Journal of Computational Fluid Dynamics 2006; 20(3-4):253-267.
25. Mathur SR, Murphy JY. A pressure-based method for unstructured meshes. Numerical Heat Transfer Part B 1997; 31:195-215.
26. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publishing Company, 1996.
27. Luo H, Baum J, Läohner R. A fast matrix-free implicit method for compressible flows on unstructured grids. Journal of Computational Physics 1998; 146:664-690.
28. Aliabadi S. Parallel finite element computations in aerospace applications. Ph.D. Thesis, University of Minnesota, 1994.
29. Stoker JJ. Water Waves. Wiley/Interscience: New York, 1957.
30. Glaister P. Difference schemes for the shallow water equations. Numerical Analysis Report 9/87. University of Reading, 1987.
31. Hudson J. Numerical techniques for morphodynamic modeling. Ph.D. Thesis, Department of Mathematics, University of Reading, October, 2001.
32. Liang SJ, Tang JH, Wu MS. Solution of shallow water equations using least squares finite element method. Acta Mechanica Sinica 2008; 24:523-532.
33. Mingham CG, Causon DM. High-resolution finite-volume method for shallow water flows. Journal of Hydraulic Engineering (ASCE) 1998; 124(6):605-614.
34. Fennema RT, Chaudhry MH. Explicit methods for 2D transient free-surface flows. Journal of Hydraulic Engineering (ASCE) 1990; 116(11):1013-1034.