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We consider the Cauchy problem for a one-dimensional homogeneous system of poroelasticity equations described by three elastic parameters in a reversible hydrodynamic approximation. We find a solution to the Cauchy problem in the form of the d'Alembert formula and show the influence of porosity on the acoustic wave propagation. Bibliography: 5 titles., 1 Introduction For applied problems of the theory of elastic wave propagation it is often required to take into account the medium porosity, fluid saturation of the medium, and the [...]

The initial boundary value problem of the dynamics of fluid saturated porous media, described by three elastic parameters in the reversible hydrodynamic approximation, is numerically solved. A linear two-dimensional problem as dynamic equations of porous media for components of velocities, stresses and pore pressure is considered. The equations of motion are based on conservation laws and are consistent with thermodynamic conditions. In this case, a medium is considered to be ideally isotropic (in the absence of energy dissipation) and twodimensional heterogeneous with respect to space. For a numerical solution of the dynamic problem of poroelasticity we use the Laguerre transform with respect to time and the finite difference technique with respect to spatial coordinates on the staggered grids with fourth order of accuracy. The description of numerical implementation of the algorithm offered is presented, and its characteristics are analyzed. Numerical results of the simulation of seismic wave fields for the test layered models have been obtained on the multiprocessor computer.

The numerical implementation of the classical model of thermal convection in a viscous compressible fluid in a finite domain is considered. Difference approximation carried out by the control volume method. The comparison of the results of test calculations with the reference results of the convection simulation of incompressible fluid in the rectangular domain is made.

The solution to equations of two viscous homogeneous incompressible fluid media with the pressure phase equilibrium in the case of a constant phase is obtained. The influence of the physical phase densities, saturation, volume and viscosity of substances constituting a two-phase continuum in the flow velocity and pressure is shown. Also, the solution admitting a limiting transition to the known solution of the problem of a flow of a viscous incompressible single-phase medium is constructed.

The form of the equation of motion of porous media in terms of velocities, stresses and pressure as symmetric t-hyperbolic (in the sense of Friedrichs) system has been obtained.