zbMATH — the first resource for mathematics

A projection method for constructing a mass conservative velocity field. (English) Zbl 0953.76045
Summary: We develop a velocity projection method that is both accurate and mass conservative element-by-element method on a projected grid. The velocity correction is expressed as gradient of a scalar pressure field, and the resultant Poisson equation is solved using a mixed/hybrid finite element method and lowest-order Raviart-Thomas spaces. The conservative projection method is applied to the system of shallow water equations, and a theoretical error estimate is derived.

76M10 Finite element methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
Full Text: DOI
[1] Brezzi, F.; Fortin, M., Mixed and hybrid finite element methods, (1991), Springer-Verlag New York · Zbl 0788.73002
[2] Cerco, C.F.; Cole, T., User’s guide to the CE-QUAL-ICM three-dimensional eutrophication model, (), Release Version 1.0
[3] R.S. Chapman, T. Gerald and M.S. Dortch, Development of unstructured grid linkage methodology and software for CE-QUAL-ICM, Private communication.
[4] S. Chippada, C.N. Dawson, M.L. Martínez and M.F. Wheeler, Finite element approximations to the system of shallow water equations, Part I: Continuous time a priori error estimates, SIAM J. Numer. Anal., to appear. · Zbl 0910.76034
[5] King, I.P.; Norton, W.R., Recent application of RMA’s finite element models for two-dimensional hydrodynamics and water quality, ()
[6] Kolar, R.; Gray, W.G.; Westerink, J.J., Boundary conditions in shallow water models—an alternative implementation for finite element codes, Int. J. numer. methods fluids, 22, 7, 603-618, (1996) · Zbl 0889.76036
[7] Lynch, D.R.; Gray, W., A wave equation model for finite element tidal computations, Comput. fluids, 7, 207-228, (1979) · Zbl 0421.76013
[8] Luettich, R.A.; Westerink, J.J.; Scheffner, N.W., ADCIRC: an advanced three-dimensional circulation model for shelves, coasts and estuaries, ()
[9] W.R. Norton, I.P. King and G.T. Orlob, A finite element model for lower granite reservoir, Water Resource Engineers, Inc., Walnut Creek, CA.
[10] Raviart, R.A.; Thomas, J.M., A mixed finite element method for 2nd order elliptic problems, mathematical aspects of the finite element method, (), 292-315
[11] Weiyan, T., Shallow water hydrodynamics, ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.