Poster

We integrate the above system over [ ]j j ×+1 [ ]n n+1 :

u u x f u d

f u d

+ += − Δ ⎡ ⎣⎢

−

1 ( ))

( ))

τ

τ

τ

τ τ ⎤ ⎦ ,+

(4)

where j nu + 12 and js + 12( )t denote the cell averages:

u x

u t dx

s x

s x t dx

=

Δ ,

=

Δ ,

( )x n,

( )t ( (u )) (5)

1 INTRODUCTION

Shallow water equations are widely used to model flows in rivers and coastal areas. For practical applications the inclusion of a non-flat bottom topography is required. Central schemes allow a simpler reconstruction of the numerical fluxes because the discontinuities in the pointwise solution, produced by the reconstruction algorithm, are located at the center of the staggered control volumes. In this paper we present an extension of the central non-oscillatory Runge-Kutta scheme given in Balaguer (2011) to solve the shallow water equations over a movable non-flat bed described in Caleffi et al. (2007).