Some observations regarding the stationary Buckley–Leverett equation

The basic hyperbolic-elliptic black-oil model describes oil-water displacement in a porous medium. Given its mathematical complexity, there is a need for particular simple solutions for validation of numerical methods. We present a class of stationary solutions, which are easy to compute, and in many cases are given by explicit formulae. These solutions are constructed by a nonlinear coupling of two linear equations, an elliptic pressure equation and a hyperbolic saturation equation.