A method is described for a method for depositional modeling dependent on geological boundary conditions including receiving a process-based depositional model of a siliciclastic formation; determining a type of boundary condition at each boundary of the process-based depositional model wherein the boundary condition on at least one boundary is one of a flux-preserving boundary condition or a discrete boundary condition and wherein the boundary condition accounts for at least one of time-varying inflow of water and sediments into the process-based depositional model, time-varying outflow of water and sediments out of the process-based depositional model, and downstream controls; modeling rates of sediment and water flow over time, dependent on the boundary condition, to create a modeled depositional system; and analyzing the modeled depositional system to identify potential hydrocarbon reservoirs. The method may be executed by a computer system.