Solving the Buckley–Leverett equation with a random coefficient of porosity

The Buckley–Leverett equation with a random coefficient of porosity is considered. In order to analyze the equation, a combination of analytical (the method of characteristics) and numerical (upwind and hybrid difference schemes) approaches is used. An explicit expression for the stochastic characteristics of the Buckley–Leverett equation is obtained. The statistical parameters of breakthrough time are considered. A comparison between the analytical estimates and the numerical results is discussed.