Simulation methods of solute transport in cross-fractures include analytical and numerical schemes. provided an analytical solution for solute transport in 2-D perpendicular fractures; however, their method can only be applied to simple boundary conditions. In fact, fracture distribution and geometric characteristics are considerably more complex compared to fractured rocks matrices. It is difficult to deduce an analytical solution to the problem of solute transport in cross-fracture or in a fracture network. Therefore, a numerical scheme is usually employed to simulate the behavior of cross-fractures. used FEM to solve the Nervier-Stokes equation in a cross-fracture. Also, a complex pipe network model was used to simulate its hydraulic and migration properties. Except for these routine numerical methods, some new, or modified, schemes were proposed to solve mathematical models of solute transport. proposed a new