Performance of finite volume solutions to the shallow water equations with shock‐capturing schemes

Abstract

SUMMARYNumerical methods have become well established as tools for solving problems in hydraulic engineering. In recent years the ÿnite volume method (FVM) with shock capturing capabilities has come to the fore because of its suitability for modelling a variety of types of ow; subcritical and supercritical; steady and unsteady; continuous and discontinuous and its ability to handle complex topography easily.This paper is an assessment and comparison of the performance of ÿnite volume solutions to the shallow water equations with the Riemann solvers; the Osher, HLL, HLLC, ux di erence splitting (Roe) and ux vector splitting. In this paper implementation of the FVM including the Riemann solvers, slope limiters and methods used for achieving second order accuracy are described explicitly step by step. The performance of the numerical methods has been investigated by applying them to a number of examples from the literature, providing both comparison of the schemes with each other and with published results. The assessment of each method is based on ÿve criteria; ease of implementation, accuracy, applicability, numerical stability and simulation time. Finally, results, discussion, conclusions and recommendations for further work are presented.

A CIP/multi‐moment finite volume method for shallow water equations with source terms

“…To compare with the numerical results given in [28] where numerical tests of shallow water equations by several well-established Riemann solvers are reported, we ran again the test with a 41×41 mesh and give the profiles of h, u and v on the cross-section of x = 92.5 m in Figure 11. It is observed that the present model has competitive numerical accuracy in simulating 2D bore shock wave.…”

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

“…FVMs of second-order accuracy for shallow water model based on flux-vector splitting and fluxdifference splitting were reported in Anastasiuo and Chan [2], Burguete and Navarro [7], Lin et al [23] and Brufau et al [6]. Erduran et al [11] evaluated and reviewed some existing approximate Riemann solvers for shallow water equations.…”

A Computational Modeling for Semi-Coupled Multiphase Flow in Atmospheric Icing Conditions

“…Although the implementation of explicit schemes is much easier than that of implicit schemes, explicit schemes require careful time step selection in order to fulfill the stability requirement. The semicoupled algorithm in this study is calculated under the maximum allowable time steps used in the work of Erduran et al (2002). The local time stepping for the temporal discretization is achieved using the fifth stage Runge-Kutta scheme.…”