A computer-based method for simulating evolution of a sedimentary basin, comprising: (a) determining at each map point a flow template and at least one sediment concentration template based on: a depth-averaged flow velocity and one or more depth-averaged sediment concentrations for associated classes of grain size, each of said depth-averaged flow velocity and one or more depth-averaged sediment concentrations being for that map point at a given time step; (b) applying at each map point the flow template to the depth-averaged flow velocity and the at least one sediment concentration template to the one or more depth-averaged sediment concentrations to obtain a vertically-distributed flow velocity profile and one or more vertically-distributed sediment concentration profiles for that map point, thereby reconstructing a 3D flow velocity field and one or more 3D sediment concentration fields for associated classes of grain size at the given time step; (c) using the 3D flow velocity field and the one or more 3D sediment concentration fields to calculate at each map point a fluid flux and one or more sediment fluxes for associated classes of grain size; (d) updating at each map point the flow velocity profile and the one or more sediment concentration profiles based on a divergence of the fluid flux and one or more divergences of the one or more sediment fluxes at that map point at the given time step; (e) computing at each map point the depth-averaged flow velocity and the one or more depth-averaged sediment concentrations by integrating the flow velocity profile and the one or more sediment concentration profiles for that map point at the given time step, thereby obtaining an updated 2D flow velocity field and an updated one or more 2D sediment concentration fields; (f) deriving from the one or more sediment concentration profiles a center of gravity for each map point; and (g) solving a set of two-dimensional flow equations based on the updated 2D flow velocity field, the updated one or more 2D sediment concentration fields, the center of the gravity, and flow height, to calculate, at each map point, the depth-averaged flow velocity at a next time step; and wherein the method further comprises using the simulation to select locations for new wells, estimate hydrocarbon reserves, and/or plan reservoir-development strategies. (a) determining at each map point a flow template and at least one sediment concentration template based on: a depth-averaged flow velocity and one or more depth-averaged sediment concentrations for associated classes of grain size, each of said depth-averaged flow velocity and one or more depth-averaged sediment concentrations being for that map point at a given time step; a depth-averaged flow velocity and one or more depth-averaged sediment concentrations for associated classes of grain size, (b) applying at each map point the flow template to the depth-averaged flow velocity and the at least one sediment concentration template to the one or more depth-averaged sediment concentrations to obtain a vertically-distributed flow velocity profile and one or more vertically-distributed sediment concentration profiles for that map point, thereby reconstructing a 3D flow velocity field and one or more 3D sediment concentration fields for associated classes of grain size at the given time step; (c) using the 3D flow velocity field and the one or more 3D sediment concentration fields to calculate at each map point a fluid flux and one or more sediment fluxes for associated classes of grain size; (d) updating at each map point the flow velocity profile and the one or more sediment concentration profiles based on a divergence of the fluid flux and one or more divergences of the one or more sediment fluxes at that map point at the given time step; (e) computing at each map point the depth-averaged flow velocity and the one or more depth-averaged sediment concentrations by integrating the flow velocity profile and the one or more sediment concentration profiles for that map point at the given time step, thereby obtaining an updated 2D flow velocity field and an updated one or more 2D sediment concentration fields; (f) deriving from the one or more sediment concentration profiles a center of gravity for each map point; and (g) solving a set of two-dimensional flow equations based on the updated 2D flow velocity field, the updated one or more 2D sediment concentration fields, the center of the gravity, and flow height, to calculate, at each map point, the depth-averaged flow velocity at a next time step; and