Method for simulation of filtration problem with the jumps of saturation

The authors offer to use the characteristic – interpolation method to obtain the solution of classical one – dimensional Backley–Lewerett problem, describing the process of displacement oil by water. It is shown that the developed method is the second order consistency for smooth solutions, reproduces well the front location, conserves the monotony of the solution and the saturation integral. The method is demonstrated on some model problems.