Naslov
Comparison of some implicit and explicit schemes for open channel flow equations

Autori
Sopta, Luka ; Kranjčević, Lado ; Vuković, Senka

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of 4th International Congress of Croatian Society of Mechanics / Matejiček, Franjo - Bizovac : Grafika Osijek, 2003, 275-282

Skup
4th International Congress of Croatian Society of Mechanics

Mjesto i datum
Bizovac, Hrvatska, 18.09.2003. - 20.09.2003

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
open channel flow; explici numerical scheme; implicit numerical scheme

Sažetak
When deciding whether to employ explicit or implicit approach in numerical approximation of open channel flow equations one has to bear in mind that explicit methods are generally easier to program, and require less computational effort per each time step than implicit methods. Explicit methods solve for one point at a time in certain time step - that is, one equation and one unknown. The main drawback of the explicit approach is that the unknown node must be within the zone of dependency of the nodes that are used to approximate the derivatives at the known time line – otherwise, the method will be unstable. Therefore, maximal time step is bound by Courant Friedrichs Lewy (CFL) condition. Implicit methods solve for the unknowns in a domain simultaneously, requiring solution of simultaneous algebraic equations. The advantage is that matrix of a linear system to be solved at each time level has its arguments from the new time level n+1 and thus the unknown nodes are always in the zone of influence. Generally, implicit methods also include data values from previous time level n but they come to the right hand side (RHS) of the linear system to be solved. Implicit schemes will yield convergence in a smaller number of time steps, since the time step is no longer constrained by a stability limit but on the other hand they require more computational effort consequent upon the need to solve block tridiagonal system of equations per each time step (providing finite difference approximation is employed). Use of implicit or explicit numerical method is also dependent upon the fact whether the objective of calculation is simply to reach steady state or analysis of transient solution is needed.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

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