Abstract
We study the significance of the spatial reconstruction when solving the one dimensional shallow water equations using a finite volume method. For that aim, we implement the explicit forward Euler method for temporal integration while the spatial discretization is performed by finite volume method. We compare the results of constant spatial reconstruction with those of linear spatial reconstruction. The numerical tests include the steady state of a lake at rest, the steady state of moving water and an unsteady state of dam break problem. It is shown that the spatial reconstruction has a significant role in the accuracy of the finite volume method. 1412 Noor Hidayat, Suhariningsih, Agus Suryanto and Sudi Mungkasi
Highlights
The free surface, unsteady water flow is modeled by the well-known Saint-Venant equations
In this paper we investigate the significance of spatial reconstruction in finite volume methods when solving the shallow water equations
We recall a finite volume method proposed in [5, 7], which was developed for steady state problems
Summary
The free surface, unsteady water flow is modeled by the well-known Saint-Venant equations. This model is called the shallow water (wave) equations. Finite difference methods are based on the differential form of the equations. They may lead to some difficulties when we want to resolve discontinuities, because differential equations assume that solutions are smooth. Finite volume methods are based on the integral form of the equations. In this paper we investigate the significance of spatial reconstruction in finite volume methods when solving the shallow water equations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
