1. A method of enhancing a geologic model of a subsurface region, comprising: (a) obtaining a bed topography of the subsurface region, the bed topography defined by a plurality of cells in a computer system, each of the plurality of cells having an elevation associated with its cell center; (b) representing the bed topography as a cell-centered piecewise constant representation based on the elevations associated with the plurality of cells; (c) reconstructing the bed topography to produce a spatially continuous surface; (d) calculating, with the computer system, flux and gravitational force-related source terms based on the reconstructed bed topography; (e) calculating fluxes between at least two of the cells, with the computer system, taking into account variations of the bed topography across a face between the at least two of the cells; (f) predicting at least one of fluid flow, deposition of sediments onto the bed, and erosion of sediments from the bed using the fluxes and gravitational force-related source terms; (g) inputting the predicted at least one of fluid flow, deposition and erosion into the geologic model of the subsurface region; (h) using the geologic model to predict characteristics of the subsurface region; (i) outputting the predicted characteristics of the subsurface region; and (j) extracting hydrocarbons based on the outputted predicted characteristics of the subsurface region.