Lax-Wendroff Richtmyer finite element
and Roe finite volume scheme for steady
two-dimensional free – surface flows
M. Mezouari1*, F. Boushaba2, M. Boulerhcha1, I. Elmahi2
1 COSTE, Département de Physique, Faculté des Sciences, BP 717, 60000 Oujda, MOROCCO
2 EMSN, ENSA, Université Mohamed Premier Oujda , MOROCCO
* Corresponding author: E-mail: email@example.com
Received: 12 January 2011; revised version accepted: 26 July 2011
Two explicit numerical schemes, Lax-Wendroff Richtmyer in finite element and Roe in finite volume version, are applied to calculate steady, two dimensional depth averaged Saint-Venant equations with source terms. Both schemes are formally second order accurate and conditionally stable. For the Roe scheme, the second order in space is reached by a MUSCL technique and slope limiters to preserve the TVD properties. To take into account the source terms in the equations, a semi-implicit splitting algorithm is introduced. The objective of this paper is to make comparisons between these two schemes over a wide variety of hydraulic engineering problems: flow with Oblique Hydraulic Jump, flow in converging channel and dam break in a river.
Keywords: Saint-Venant equations; Source term; Finite element; Lax-Wendroff Richtmyer scheme; Roe scheme; Finite volume; MUSCL; Numerical diffusion; Riemann solver.