Numerical implementation of the initial-boundary value problem for nonlinear the onedimensional equations of poroelasticity for the water-ice system

Abstract

Summary This article is devoted to the problem of propagation of elastic transverse oscillations in a two-phase medium consisting of water and ice (ice impregnated with water). If we consider ice as a kind of porous homogeneous medium with constant partial density, then it becomes possible to apply the problems of the theory of filtration to the water-ice medium. In this paper, we consider one of the possible formulations of the direct problem modeling the propagation of a signal in this medium is considered. The initial-boundary value problem for a one-dimensional nonlinear system of poroelasticity equations is solved by numerical method on the basis of an explicit-difference scheme. A series of numerical calculations for a trial model of the media is presented.The aim of the paper is to describe the approach to the study of water-ice media using the equations of filtration theory. The object of the study is the propagation of wave oscillations in such media. Such fluctuations can have different nature (seismic, acoustic, etc.). For example, it is of interest to use this approach to model the propagation of sea waves in the ice of the initial stage of ice formation.