The accuracy and efficiency of a class of finite volume methods are investigated for
numerical solution of morphodynamic problems in one space dimension. The governing
equations consist of two components, namely a hydraulic part described by the shallow
water equations and a sediment part described by the Exner equation. Based on different
formulations of the morphodynamic equations, we propose a family of three finite volume
methods. The numerical fluxes are reconstructed using a modified Roe's scheme that
incorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamic
system. A well-balanced discretization is used for the treatment of the source terms.
The method is well-balanced, non-oscillatory and suitable for both slow and rapid
interactions between hydraulic flow and sediment transport. The obtained results for
several morphodynamic problems are considered to be representative, and might be helpful
for a fair rating of finite volume solution schemes, particularly in long time computations.