Continuous symmetries for an equation (differential or difference) give opportunities to obtain a family of solutions if one particular solution (not invariant) is known. This principle lies in the basis of the presented novel method of fast numerical solutions calculations for finite-difference schemes. The method allows to obtain families of numerical solutions for difference schemes of differential equations for different processes. The main purpose of this report is to present the novel method of numerical solutions calculations using continuous symmetries of difference schemes for some particular differential equations of multiphase flow in porous media which are generalizations of the Buckley-Leverett problem.