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A new approach is considered for increasing the order of accuracy of the grid-characteristic method in the region of coefficient jumps. The approach is based on piecewise polynomial interpolation for schemes of the second and third orders of accuracy for the case where the interface between the media is consistent with a finite-difference grid. The method is intended for numerical simulation of the propagation of dynamic wave disturbances in heterogeneous media. Systems of hyperbolic equations with variable coefficients are used to describe the considered physical processes. The description of the numerical method and the results of its testing are given. [ABSTRACT FROM AUTHOR]

The grid-characteristic method on structured grids is applied to various problems related to railway-traffic safety, as well as to obtain results of full wave modeling using this method and analyzing them for a better understanding of the physical processes occurring under conditions of heavy and high-speed traffic on various sections of the track. The problem involves the consideration of traffic on a ballasted and ballastless bridge desk. In the course of computer simulation, various wave fields and dynamic distributions of pressure and components of the Cauchy stress tensor are obtained during the traffic. The calculation time during which the propagation of wave processes occurs in various bridge structures is estimated. The results obtained give an idea of wave phenomena during the traffic in the area of bridges and along the railway track as a whole. [ABSTRACT FROM AUTHOR]

The problem of tsunami warning and the use of the grid-characteristic method developed for studying wave processes in heterogeneous media is addressed. A multilayer geological model with curved boundaries and contrasting elastic parameters is considered. Various seismic survey methods, as well as different geometries of the boundaries, different values of rock densities, and various longitudinal and shear wave velocities, are examined. The boundary value problem is numerically solved jointly for the elastic and acoustic wave equations (seismic wave propagation in rocks and water layer, respectively). We use the numerical grid-characteristic method with combined structured curvilinear and regular computational grids. The wave velocity fields (velocity as derivative of displacement) and stress fields are calculated and analyzed. Synthetic seismograms are calculated for the coastal zone. It is found that some specific features of seismograms and some wave modes can be used for tsunami warning. The optimal parameters of seismic surveying are determined. Numerical simulation of wave propagation effects is used for these purposes. The proposed numerical grid-characteristic method can be used in forward numerical modeling in order to interpret seismograms recorded in the coastal zone. [ABSTRACT FROM AUTHOR]

This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer fractured media. The dynamic processes are described using the defining system of equations in the partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic method on curvilinear structural grids. The fractured nature of the medium is accounted for by explicitly selecting the boundaries of individual cracks and setting special boundary conditions in them. Various models of heterogeneous deformed media with a fractured structures are considered: a homogeneous medium, a medium with horizontal boundaries, a medium with inclined boundaries, and a medium curvilinear boundaries. The wave fields detected on the surface are obtained, and their structures are analyzed. It is demonstrated that it is possible to detect the waves scattered from fractured media even in the case of nonparallel (inclined and curvilinear) boundaries of geological layers. [ABSTRACT FROM AUTHOR]

The goal of this paper is the numerical solution of direct problems concerning hydrocarbon seismic exploration on the Arctic shelf. The task is addressed by solving a complete system of linear elasticity equations and a system of acoustic field equations. Both systems are solved by applying the grid-characteristic method, which takes into account all wave processes in a detailed and physically correct manner and produces a solution near the boundaries and interfaces of the integration domain, including the interface between the acoustic and linear elastic media involved. The seismograms and wave patterns obtained by numerically solving these systems are compared. The effect of ice structures on the resulting wave patterns is examined. [ABSTRACT FROM AUTHOR]

For wave propagation in heterogeneous media, we compare numerical results produced by grid-characteristic methods on structured rectangular and unstructured triangular meshes and by a discontinuous Galerkin method on unstructured triangular meshes as applied to the linear system of elasticity equations in the context of direct seismic exploration with an anticlinal trap model. It is shown that the resulting synthetic seismograms are in reasonable quantitative agreement. The grid-characteristic method on structured meshes requires more nodes for approximating curved boundaries, but it has a higher computation speed, which makes it preferable for the given class of problems. [ABSTRACT FROM AUTHOR]

Results of the numerical simulation of mechanical processes occurring in biological tissues under dynamic actions are presented. The grid-characteristic method on unstructured grids is used to solve the system of equations of mechanics of deformable solids; this method takes into account the characteristic properties of the constitutive system of partial differential equations and produces adequate algorithms on interfaces between media and on the boundaries of integration domains. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article presents a mathematical research which describes a grid-characteristic approach on unstructured tetrahedral grids. Details include numerical algorithms, a set of intersecting cracks on a tetrahedral grid, and the wave-response to a set of macrocracks. It concludes the construction of a grid-characteristic method for numerical solutions of problems related to seismology and seismic prospecting.

The article presents a mathematical research which introduces a grid-characteristic method for the numerical simulation of the effects of anisotropic media on seismic wave propagation. Details include the statement of the problem and numerical results for the wave pattern in elastic wave propagation through horizontally transversal and heterogenous anisotropic media. It concludes the development of the grid method through studying the system of equations in anisotropic medium.