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As discussed before, there are several numerical methods that may be used for the integration of de Saint Venant equations. Of these methods, the finite-difference methods have been utilized extensively in the literature and details of some of these methods are outlined in this chapter. Either a conservation or nonconservation form of the governing equations may be used in some methods whereas only one of these forms may be used in others. A conservation form should be preferred, since it conserves various quantities better and it simulates the celerity of wave propagation more accurately than the nonconservation form.
First, a number of commonly used terms are discussed. Then, a number of typical explicit finite-difference schemes are presented and the inclusion of boundary conditions in these schemes is outlined and the stability of the scheme is discussed. These schemes includes: the Unstable scheme, Diffusive scheme, and MacCormack scheme which is a second-order accurate in space and time and is capable of capturing the shocks without isolating them. Then, three implicit finite-difference methods are presented including Preissmann scheme, Beam and Warming scheme, and Vasiliev Scheme. The consistency of a numerical scheme is briefly discussed and the stability conditions are then derived. The results computed by different schemes are compared.
As discussed before, there are several numerical methods that may be used for the integration of de Saint Venant equations. Of these methods, the finite-difference methods have been utilized extensively in the literature and details of some of these methods are outlined in this chapter. Either a conservation or nonconservation form of the governing equations may be used in some methods whereas only one of these forms may be used in others. A conservation form should be preferred, since it conserves various quantities better and it simulates the celerity of wave propagation more accurately than the nonconservation form.
First, a number of commonly used terms are discussed. Then, a number of typical explicit finite-difference schemes are presented and the inclusion of boundary conditions in these schemes is outlined and the stability of the scheme is discussed. These schemes includes: the Unstable scheme, Diffusive scheme, and MacCormack scheme which is a second-order accurate in space and time and is capable of capturing the shocks without isolating them. Then, three implicit finite-difference methods are presented including Preissmann scheme, Beam and Warming scheme, and Vasiliev Scheme. The consistency of a numerical scheme is briefly discussed and the stability conditions are then derived. The results computed by different schemes are compared.
FINITE-DIFFERENCE METHODS
Chaudhry, M. Hanif (author)
Open-Channel Flow ; Chapter: 14 ; 381-413
2022-01-01
33 pages
Article/Chapter (Book)
Electronic Resource
English
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