I. B. Petrov

Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step

The purpose of the present paper is to develop a grid-characteristic method for high-performance computer systems using unstructured tetrahedral hierarchical meshes, a multiple time step and the high-order interpolation for simulating complex spatial dynamic processes in heterogeneous environments. This method has the precise formulation of contact conditions and is suitable for the physically correct solution of seismology and seismic prospecting problems in complex heterogeneous environments. The use of the hierarchical meshes allows us to take into account a large number of nonhomogeneous inclusions (cracks, cavities, etc.). The use of this grid-characteristic method makes it possible to use a multiple time step and thereby increase productivity and significantly reduce the computation time. The methods developed for high-order interpolation on unstructured tetrahedral meshes can solve the problems of seismology and seismic prospecting with approximation in space of up to the fifth degree (inclusive).

High-performance computer simulation of wave processes in geological media in seismic exploration

A class of problems arising in seismic exploration are investigated, namely, seismic signal propagation in multilayered geological rock and near-surface disturbance propagation in massive rock with heterogeneities, such as empty or filled fractures and cavities. Numerical solutions are obtained for wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock, which can be manifested near a seismic gap or a wellbore. All types of explosion-generated elastic and elastoplastic waves and waves reflected from fractures and the boundaries of the integration domain are analyzed. The identification of waves in seismograms recorded with near-surface receivers is addressed. The grid-characteristic method is used on triangular, parallelepipedal, and tetrahedral meshes with boundary conditions set on the rock-fracture interface and on free surfaces in explicit form. The numerical method proposed is suitable for the study of the interaction between seismic waves and heterogeneous inclusions, since it ensures the most correct design of computational algorithms on the boundaries of the integration domain and at media interfaces. A parallel software code implemented with the help of OpenMP and MPI was used to execute computations on parallelepipedal and tetrahedral grids.

Numerical simulation of seismic activity by the grid-characteristic method

Seismic activity in homogeneous and layered enclosing rock masses is studied. A numerical mechanical-mathematical model of a hypocenter is proposed that describes the whole range of elastic perturbations propagating from the hypocenter. Synthetic beachball plots computed for various fault plane orientations are compared with the analytical solution in the case of homogeneous rock. A detailed analysis of wave patterns and synthetic seismograms is performed to compare seismic activities in homogeneous and layered enclosing rock masses. The influence exerted by individual components of a seismic perturbation on the stability of quarry walls is analyzed. The grid-characteristic method is used on three-dimensional parallelepipedal and curvilinear structured grids with boundary conditions set on the boundaries of the integration domain and with well-defined contact conditions specified in explicit form.

Wave responses from oil reservoirs in the Arctic shelf zone

We consider the appearance of scattered PP-waves, SS-waves, scattered converted PS-waves, and SP-waves reflected from the reservoirs in the Arctic shelf zone and wave responses from them in the water column when the source and receiver are located near the water surface. We obtained a numerical solution of the direct problems of seismic prospecting in the shelf zone with a reservoir and without it. The solution was obtained using the grid-characteristic method, which makes possible to model the wave processes in detail.

Numerical modeling of dynamic wave effects in rock masses

Spatial dynamic wave effects occurring in rocks with ravines and caverns were studied. The influence exerted by the explosion type and the cavern-to-ravine distance on the formation of spatial dynamic wave patterns and seismograms was analyzed in the case of horizontal and vertical reception lines. The gridcharacteristic method and the full wave joint numerical modeling of elastic and acoustic waves were used.

Virtual blunt injury of human thorax: age-dependent response of vascular system

Abstract This work is the numerical study of the age-dependent responses of the vascular system under low-mass high-speed impact scenario. The grid-characteristic method on the adaptive mesh model of the human thorax is the numerical tool of the study. Due to the lack of valid vascular injury criteria, the numerical model only provides information on injury risk. The numerical simulation demonstrates that an older age changes significantly the vascular response and increases the risk of aorta injury. We focused on the aorta because its rupture is the general consequence of vehicle accidents (great mass impacts at relatively low velocity). Our numerical results are in good agreement with previous studies of great-mass low-speed blunt thorax impact.

Monitoring the State of the Moving Train by Use of High Performance Systems and Modern Computation Methods

The objective of this work has been to study the propagation of elastic waves in rails. It presents the comparison of calculations obtained by the grid-characteristic and discontinuous Galerkin methods. The propagation of elastic waves in the presence and absence of the karst inclusion in the ground under the embankment, diagnosed in these cases from the rails, are compared. The wave pictures and diagnosed signals for four types of defects of a fractured character: vertical and horizontal head layering, cross fracture in the head and cracks in the rail web are given. The grid-characteristic method on the curvilinear structural meshes and the discontinuous Galerkin method on the nonstructured triangular meshes make it possible to solve efficiently the tasks on monitoring the state of the moving train and rail, including a great number of integrity violations, dynamic interactions in the train-rail system, and obtain the full wave picture.

Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes

Wave propagation in fractured rock in the course of seismic exploration is studied. The grid-characteristic method on hexahedral meshes is extended to the case of an elastic medium with empty and fluid-saturated cracks. The crack effect on wave propagation in the medium is taken into account by introducing cracks at the stage of grid generation with boundary conditions and conditions on the crack edges specified in explicit form. This method is used to obtain wave patterns near an extended inclined crack. The problem of numerically computing the seismic effect produced by a cluster of vertical and subvertical cracks is given in a complete three-dimensional formulation. The structure of the resulting pattern and the influence exerted by the crack-filling substance on the signal recorded on the surface are examined.

Numerical simulation of processes in solid deformable media in the presence of dynamic contacts using the grid-characteristic method

Several problems of dynamic deformation in the presence of movable contacting surfaces are considered. A grid-characteristic method is adapted using two-dimensional irregular triangular grids and a hybrid scheme of the first or second order of approximation. An algorithm for the calculation of sliding and static friction is proposed. We obtained the numerical solution for problems of wheel rolling, generation of shear waves, piston acceleration in a pipe, and ricochet.

Grid-characteristic method on unstructured tetrahedral meshes

The goal of this paper is to develop a grid-characteristic method intended for high-performance computer systems and implemented on unstructured tetrahedral hierarchical meshes with the use of a multiple time step and high-order interpolation, including interpolation with a limiter, piecewise parabolic interpolation, and monotone interpolation. The method is designed for simulating complex three-dimensional dynamical processes in heterogeneous media. It involves accurately stated contact conditions and produces physically correct solutions of problems in seismology and seismic exploration. Hierarchical meshes make it possible to take into account numerous inhomogeneous inclusions (cracks, cavities, etc.) and to solve problems in a real-life formulation. The grid-characteristic method enables the use of a multiple time step. As a result, the computation time is considerably reduced and the efficiency of the method is raised. The method is parallelized on a computer cluster with an optimal use of system resources.