A mass-conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

International Journal for Numerical Methods in Fluids

Volumn 81, Issue 3, 2016, Pages 151-177

  Canestrelli, Alberto ^a   Spruyt, Aukje ^b   Jagers, Bert ^b   Slingerland, Rudy ^a   Borsboom, Mart ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b DELTARES   (Netherlands)

Author keywords

Finite difference; Free surface; Hydrodynamics; Immersed boundary; Implicit; Shallow water

Indexed keywords

CELLS; CYTOLOGY; FINITE DIFFERENCE METHOD; HYDRODYNAMICS; NUMERICAL METHODS;

3-D SHALLOW-WATER EQUATIONS; CONTINUITY EQUATIONS; FREE SURFACES; IMMERSED BOUNDARY; IMPLICIT; NUMERICAL SOLUTION; SHALLOW WATER EQUATIONS; SHALLOW WATERS;

EQUATIONS OF MOTION;

EID: 84954483886     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.4180     Document Type: Article

References (44)

1. Anastasiou K, Chan CT. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. International Journal for Numerical Methods in Fluids 1997; 24(11):1225-1245.
2. Fujihara M, Borthwick AGL. Godunov-type solution of curvilinear shallow-water equations. Journal of Hydraulic Engineering ASCE 2000; 126(11):827-836.
3. Bandringa H. Immersed boundary methods. MSc Thesis, University of Groningen, the Netherlands, 2010.
4. Mittal R, Iaccarino G. Immersed boundary methods. Annual Review of Fluid Mechanics 2005; 37:239-261.
5. Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. Journal of Computational Physics 2003; 190:572-600.
6. Zheng L, Hedrick TL, Mittal R. Time-varying wing-twist improves aerodynamic efficiency of forward flight in butterflies. PloS One 2013; 8(1):e53060.
7. Mittal R, Zheng X, Bhardwaj R, Seo JH, Bielamowicz S. Toward a simulation-based tool for the treatment of vocal fold paralysis. Frontiers of Physics 2011; 2:1-15.
8. Seo JH, Mittal R. A coupled flow-acoustic computational study of bruits from a modeled stenosed artery. Medical & Biological Engineering Computing, 2012; 50(10):1025-1035.
9. Zheng X, Seo JH, Vedula V, Abraham T, Mittal R. Computational modeling and analysis of intracardiac flows in simple models of the left ventricle. European Journal of Mechanics - B/Fluids 2012; 35:31-39.
10. An H, Yu S. Well-balanced shallow water flow simulation on quadtree cut cell grids. Advances in Water Resources 2012; 39:60-70.
11. Causon DM, Ingram DM, Mingham CG, Yang G, Pearson RV. Calculation of shallow water flows using a Cartesian cut cell approach. Advances in Water Resources 2000; 23(5):545-562.
12. Causon DM, Ingram DM, Mingham CG. A Cartesian cut cell method for shallow water equations with moving boundaries. Advances in Water Resources 2001; 24:889-911.
13. Ingram DM, Causon DM, Mingham CG. Developments in Cartesian cut cell methods. Mathematics and Computing in Simulation 2003; 61:5, 61-72.
14. Kim H-J, Lee JW, Cho Y-S. Numerical simulation of shallow-water flow using the modified Cartesian cut-cell approach. Journal of Engineering Mechanics 2010; 136(3):399-404.
15. Liang Q, Zang J, Borthwick AGL, Taylor PH. Shallow flow simulation on dynamically adaptive cut-cell quadtree grids. International Journal for Numerical Methods in Fluids 2007; 53(12):1777-1799.
16. Altinakar M. DSS-WISE simulation-based decision support system for water infrastructural security - DSS WISE project final report, National Center For Computational Hydroscience And Engineering, Technical Report No. NCCHE-TR-2008-11, 2008.
17. Altinakar MS, McGrath MZ, Ozeren Y, Miglio E. Representation of linear terrain features in a 2D flood model with regular Cartesian mesh. Proceedings of the 2009 World Environmental & Water Resources (EWRI) Congress, ASCE, May 16-23, 2009, Kansas City, Missouri, 2009.
18. Liang Q, Borthwick AGL. Simple treatment of non-aligned boundaries in a Cartesian grid shallow flow model. International Journal for Numerical Methods in Fluids 2008; 56(11):2091-2110.
19. Seo JH, Mittal R. A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. Journal of Computational Physics 2011; 230-19:7347-7363.
20. Stelling GS, Duinmeijer SPA. A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. International Journal for Numerical Methods in Fluids 2003; 43:1329-1354.
21. Leendertse JJ. Aspects of a computer model for long period water-wave propagation. RAND Corporation Memorandum RM-5294-PR, 1967.
22. Casulli V, Zanolli P. Semi-implicit numerical modeling of nonhydrostatic free-surface problems for environmental problems. Mathematical and Computer Modelling 2002; 36:1131-1149.
23. Casulli V, Stelling GS. Numerical simulation of 3D quasi-hydrostatic free-surface flows. Journal of Hydraulic Engineering 1998; 124(7):678-686.
24. Casulli V. A semi-implicit finite difference method for nonhydrostatic, free-surface flows. International Journal for Numerical Methods in Fluids 1999; 30:425-440.
25. Deltares. Delft3D-FLOW: simulation of multi-dimensional hydrodynamic flows and transport phenomena, including sediments - user manual, 614pp., Deltares, Delft, Netherlands, 2014, online at http://oss.deltares.nl/documents/183920/185723/Delft3D-FLOW_User_Manual.pdf .
26. Uittenbogaard RE, van Kester JATM, Stelling GS. Implementation of three turbulence models in 3D-TRISULA for rectangular grids. Tech. Rep. Z81, WL|Delft Hydraulics, Delft, The Netherlands, 1992.
27. Nezu I, Nakagawa A. Turbulence in Open Channel Flows. IAHR Monograph Series, Balkema: Rotterdam, 1993.
28. Rodi W. Turbulence models and their application in hydraulics. In A State of the Art Review (3rd edn). Balkema AA: Rotterdam, Netherlands, Essex, England, 1993.
29. Bakhmetev BA. Hydraulics of open channels. Eng. Soc. Monograph. McGraw-Hill, 1932.
30. Stelling GS, Wiersma AK, Willemse JBTM. Practical aspects of accurate tidal computations. Journal of Hydraulic Engineering 1986; 112(9):802-817.
31. Stelling GS, Leendertse JJ. Approximation of convective processes by cyclic AOI methods. In M. L. Spaulding, K. Bedford and A. Blumberg, eds., Estuarine and coastal modeling, Proceedings 2nd Conference on Estuarine and Coastal Modelling, ASCE, pages 771-782 1992. Tampa.
32. Mittal R, Dong H, Bozkurttas M, Najjar FM, Vargas A, von Loebbecke A. A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. Journal of Computational Physics 2008; 227(10):4825-52.
33. Spruyt A, Mosselman E, Jagers B. A New Approach to River Bank Retreat and Advance in 2D Numerical Models of Fluvial Morphodynamics, RCEM2011. Tsinghua University Press: Beijing, 2011.
34. Lekien F, Haller G. Unsteady flow separation on slip boundaries. Physics of Fluids 2008; 20:1-19.
35. Stelling GS. On the construction of computational methods for shallow water flow problems. Tech. Rep. 35, Rijkswaterstaat, 1983.
36. Horritt MS. Evaluating wetting and drying algorithms for finite element models of shallow water flow. International Journal for Numerical Methods in Engineering 2002; 55:835-851.
37. Rozovskii IL. Flow of water in bends of open channels, Academy of Sciences of the Ukrainian SSR, Kiev (translated from Russian by the Israel Program for Scientific Translations, Jerusalem, 1961), 1957, 233 pp.
38. Stoker JJ. Water Waves. Interscience: New York, 1957.
39. Canestrelli A, Toro EF. Restoration of the contact surface in FORCE-type centered schemes II: non conservative one- and two-layer two-dimensional shallow water equations. Advances in Water Resources 2012a; 47:76-87.
40. Canestrelli A, Fagherazzi S, Lanzoni S. A mass-conservative centered finite volume model for solving two-dimensional two-layer shallow water equations for fluid mud propagation over varying topography and dry areas. Advances in Water Resources 2012b; 40:54-70.
41. Canestrelli A, Siviglia N, Dumbser M, Toro EF. Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed. Advances in Water Resources 2010; 33:291-303.
42. Canestrelli A, Siviglia N, Dumbser M, Toro EF. Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed. Advances in Water Resources 2009; 32:834-844.
43. Canestrelli A, Toro EF. Restoration of the contact surface in FORCE-type centered schemes I: homogeneous two-dimensional shallow water equations. Advances in Water Resources 2012c; 47:88-99.
44. Leopold LB, Wolman MG, Miller JP. Fluvial Processes in Geomorphology. W.H. Freeman and Co.: London, 1964; 522.