Vasilii Ivanovich Vasiliev

In this work, we consider a two-phase flow in heterogeneous porous media with non-equilibrium and nonlinear effects. The mathematical model is described by a coupled nonlinear system of equations for pressure, velocity, and saturation with a flow model that includes a specific time-dependent relationship of velocity and pressure. For a numerical solution, we construct a finite-volume approximation by space for flow and transport processes in heterogeneous porous media with an upwind scheme for a transport equation. We present a time approximation scheme based on the implicit approximation by time for pressure equation and explicit approximation of the saturation equation. Careful approximation of the flow term in the two-phase flow model with non-equilibrium and nonlinear effects is considered. Results are presented for two types of heterogeneous permeability with high-contrast properties in the two-dimensional formulation. Numerical investigation is presented for varying parameters of the rheological flow model.

In this work, we consider a two-phase flow in heterogeneous porous media with non-equilibrium and nonlinear effects. The mathematical model is described by a coupled nonlinear system of equations for pressure, velocity, and saturation with a flow model that includes a specific time-dependent relationship of velocity and pressure. For a numerical solution, we construct a finite volume approximation by space for flow and transport processes in heterogeneous porous media with an upwind scheme for a transport equation. We present a time approximation scheme based on the implicit approximation by time for pressure equation and explicit approximation of the saturation equation. Careful approximation of the flow term in the two-phase flow model with non-equilibrium and nonlinear effects is considered. Results are presented for two types of heterogeneous permeability with high-contrast properties in the two-dimensional formulation. Numerical investigation is presented for varying parameters of the rheological flow model.

Unlike quaternions and split quaternions, reduced biquaternions satisfy the multiplication commutative rule and are commonly used in image processing, fuzzy recognition, image compression, Hopfield neural networks, and digital signal processing. However, although algebraic techniques have been developed for the diagonalisation of quaternion and split quaternion matrices, the diagonalisation of a reduced biquaternion matrix is yet to be studied. In this study, we derive sufficient and necessary conditions for the diagonalisation of a reduced biquaternion matrix and devise two numerical methods for the diagonalisation of a reduced biquaternion matrix. These methods were derived using complex and real representations in the reduced biquaternionic algebra.