Development of boundary-element time-step scheme in solving 3D poroelastodynamics problems

Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, 23 Prospekt Gagarina, bld. 6, 603950, Nizhni Novgorod, Russia

^* Corresponding author: andrey.petrov@mech.unn.ru

Published online: 7 September 2018

Abstract

The development of time-step boundary-element scheme for the three dimensional boundaryvalue problems of poroelastodynamics is presented. The poroelastic continuum is described using Biot’s mathematical model. Poroelastic material is assumed to consist of a solid phase constituting an elastic formdefining skeleton and carrying most of the loading, and two fluid phases filling the pores. Dynamic equations of the poroelastic medium are written for unknown functions of displacement of the elastic skeleton and pore pressures of the filling materials. Green’s matrices and, based on it, boundary integral equations are written in Laplace domain. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. Boundary element scheme is based on time-step method of numerical inversion of Laplace transform. A modification of the time-step scheme on the nodes of Runge-Kutta methods is considered. The Runge-Kutta scheme is exemplified with 2-and 3-stage Radau schemes. The results of comparing the two schemes in analyzing a numerical example are presented.