1. A method for performing a drilling operation for an oil field, the oil field having a subterranean formation with geological structures and reservoirs therein, comprising: creating a finite-difference model to simulate behavior of a drilling assembly used to drill a wellbore in the drilling operation by: modeling the wellbore as a visco-elastic boundary with friction; and modeling interaction of a drill bit of the drilling assembly with rock along the wellbore using structural compliance of the tool under compressive loading and a modified Hertzian contact formulation in which contact area, reaction forces, and torque are non-linearly dependent on depth of cut, rock strength, and drill bit geometry, wherein the depth of cut is calculated using actual bit cutting advance per revolution; performing a simulation of the drilling operation using the finite-difference model; analyzing a result of the simulation to generate an analysis; and generating, using a computer processor, a modified drilling operation by selectively modifying the drilling operation within the finite-difference model based on the analysis.