In recent decades,a few Godunov-type,finite volume two-dimensional (2D) unstructured grid,coupled flow,and sediment models (GF2DUCM) have been developed for flows over erodible beds.These kinds of models are generally analyzed as a Vertex Model (VM) that define topography at the cell vertex,which can lead to the non-conservation of mass regarding flow,sediment,and bed evolution.Here,a full cellcantered variable storage method (Central Model or CM) is applied as the solution of the GF2DUCM.In this method,terrain elevation is defined at the cell centroids;this accurately describes the physical relations between the water depth and topography deformation.This approach can fully eliminate calculation errors in topography deformation at local cells caused by the interpolation of topography deformation at the cell vertex,and reduced uncertainty in the computation of the GF2DUCM.The model performance is systematically tested using a series of laboratory experiments,which demonstrate the mass conservation feature and high accuracy in reproducing hydrodynamic and morphological processes.