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A STUDY OF WELL-BALANCED FINITE VOLUME METHODS AND REFINEMENT INDICATORS FOR THE SHALLOW WATER EQUATIONS

Part of: Incompressible inviscid fluids Basic methods in fluid mechanics Partial differential equations, initial value and time-dependent initial-boundary value problems Partial differential equations, boundary value problems

Published online by Cambridge University Press:  04 September 2013

SUDI MUNGKASI
SUDI MUNGKASI*
Affiliation:
Department of Mathematics, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002, Indonesia email sudi@usd.ac.id Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia email sudi.mungkasi@anu.edu.au
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Abstract

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Keywords

finite volume methodsdam breakdebris avalancheCarrier–Greenspan solutionnumerical entropy productionweak local residualsadaptive mesh refinementshallow water equations

MSC classification

Secondary: 65M08: Finite volume methods 65N08: Finite volume methods 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M12: Finite volume methods
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 351 - 352
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Audusse, E., Bouchut, F., Bristeau, M. O., Klein, R. and Perthame, B., ‘A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows’, SIAM J. Sci. Comput. 25 (2004), 2050–2065.CrossRefGoogle Scholar
Karni, S., Kurganov, A. and Petrova, G., ‘A smoothness indicator for adaptive algorithms for hyperbolic systems’, J. Comput. Phys. 178 (2002), 323–341.CrossRefGoogle Scholar
Mungkasi, S. and Roberts, S. G., ‘On the best quantity reconstructions for a well balanced finite volume method used to solve the shallow water wave equations with a wet/dry interface’, ANZIAM J. (Electronic Supplement) 51 (2010), C48–C65.Google Scholar
Mungkasi, S. and Roberts, S. G., ‘A finite volume method for shallow water flows on triangular computational grids’. Proceedings of IEEE International Conference on Advanced Computer Science and Information System (ICACSIS) (Faculty of Computer Science, The University of Indonesia, Jakarta, 2011), 79–84.Google Scholar
Mungkasi, S. and Roberts, S. G., ‘A new analytical solution for testing debris avalanche numerical models’, ANZIAM J. (Electronic Supplement) 52 (2011), C349–C363.Google Scholar
Mungkasi, S. and Roberts, S. G., ‘Numerical entropy production for shallow water flows’, ANZIAM J. (Electronic Supplement) 52 (2011), C1–C17.Google Scholar
Mungkasi, S. and Roberts, S. G., ‘Analytical solutions involving shock waves for testing debris avalanche numerical models’, Pure Appl. Geophys. 169 (2012), 1847–1858.CrossRefGoogle Scholar
Mungkasi, S. and Roberts, S. G., ‘Approximations of the Carrier–Greenspan periodic solution to the shallow water wave equations for flows on a sloping beach’, Internat. J. Numer. Methods Fluids 69 (2012), 763–780.CrossRefGoogle Scholar
Mungkasi, S. and Roberts, S. G., ‘Behaviour of the numerical entropy production of the one-and-a-half-dimensional shallow water equations’, ANZIAM J. (Electronic Supplement) 54 (2013), C18–C33.Google Scholar
Noelle, S., Pankratz, N., Puppo, G. and Natvig, J. R., ‘Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows’, J. Comput. Phys. 213 (2006), 474–499.CrossRefGoogle Scholar
Puppo, G., ‘Numerical entropy production for central schemes’, SIAM J. Sci. Comput. 25 (2004), 1382–1415.CrossRefGoogle Scholar