Abstract
In this paper, an approximate method for solving the saturation equation in the problem of twophase nonequilibrium flow in porous media is constructed. This problem is being studied as part of the work carried out under a grant project funded by the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. AP08053189. This equation refers to an equation of the convection-diffusion type with a predominance of convection and with an additional term containing the third-order derivative of the solution. Due to the hyperbolic nature of the equation, its solution is accompanied by a number of difficulties that lead to the need for a careful choice of the solution method. One of the difficulties is the appearance of non-physical oscillations at the interface of the two phases. Three classical stabilized finite element methods (SUPG, GLS and USFEM) are compared based on computational experiments. In addition, comparative calculations were performed using several stabilization parameters due to the sensitivity of the stabilized methods to the choice of these parameters and the significant dependence of stability and accuracy on them. Methodological calculations are carried out and the results of calculations with different values of mesh configurations, stabilization parameters are presented.