Solution of equations of a one-dimensional problem on two-phase filtration in a porous medium with account of thermodynamical effects by using geometric methods (Q2202739)

An asymptotic method is proposed for constructing a solution to the one-dimensional problems of two-phase filtration of liquids in porous media which are described by the Buckley-Leverett equations, the Darcy law, and the law of conservation of energy. The method allows determining the water saturation in zero and a first approximation with respect to the parameters with a given accuracy. This method is not based on the discretization of the problem and, therefore, does not require the solution of large-scale linear systems or grinding of the grid near the shock wave. In this way, the solutions are computed for any \(x\) and \(t\) independently.