Based on shallow-water approximations the governing equations for two dimensional two-phase gravity currents over a porous substrate and some appropriate boundary conditions were introduced. With on characteristic interpolations the numerical boundary conditions were introduced and a series of exact solutions were constructed. Numerical analysis were made by using the two-step Lax scheme, second-order TVD scheme, third-order ENO scheme and fifth-order WENO scheme combined with second- and third-order TVD-Runge-Kutta method is given. It is found that for practice applications the second-order TVD scheme combined with the second-order TVD-Runge-Kutta method is an economical and suitable choice.