Numerical study of some dynamic problems of the mechanics of a deformable rigid body by the mesh-characteristic method

Petrov, Ivailo; Холодов, А. С.

doi:10.1016/0041-5553(84)90044-2

Cited by 40 publications

(14 citation statements)

References 3 publications

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“…To be able to build grid characteristic difference schemes without the procedures of matrix inversion and approximate calculation of its eigenvalues and vectors, we will use an explicit recording of matrices A j and their spectral decomposition obtained in [12].…”

Section: Canonical Recording Of Differential Equationsmentioning

confidence: 99%

Numerical study of the anisotropy of wave responses from a fractured reservoir using the grid-characteristic method

Kvasov

Petrov

2012

Math Models Comput Simul

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This work is aimed at studying the problem of subsurface disturbance propagation in a mas sive rock containing various inhomogeneities: empty or filled cracks. Numerical solutions to the prob lems of wave propagation in such substantially inhomogeneous media have been obtained. The depen dence that the parameters of the response from a fractured reservoir have on the problem parameters is studied. The latter parameters are the density of the crack location, the fractured reservoir extent, amount of cracks, the initial disturbance location, crack inclination, and disturbance frequency. The concept of response anisotropy is introduced and the dependence that the anisotropy has on the abovementioned parameters is studied. The grid characteristic method based on triangular meshes with the boundary conditions at the inter face between the rock and crack and at free surfaces is used in an explicit form. The proposed numer ical method can be used by studying the processes of interaction between seismic waves and inhomo geneous inclusions because it allows us to design most correctly the calculation algorithms at the inter faces between the integration domain and the media.

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Section: Canonical Recording Of Differential Equationsmentioning

confidence: 99%

Numerical study of the anisotropy of wave responses from a fractured reservoir using the grid-characteristic method

Kvasov

Petrov

2012

Math Models Comput Simul

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“…Одним из ограничений данных методов является невозмож-ность явного учета трещиноватых включений, характерных для нефтеносных пластов. Оно бы-ло преодолено в работах [Golubev et al, 2015;Kvasov et al, 2011;Golubev et al, 2017] с исполь-зованием сеточно-характеристического метода [Petrov et al, 1984;Magomedov et al, 1969] на структурных и неструктурных расчетных сетках.…”

Section: Introductionunclassified

Estimation of anisotropy of seismic response from fractured geological objects

Golubev¹,

Хохлов²

2018

CRM

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“…T is the vector of variables, f is the right-hand side of the same dimension, A i are the matrices of ninth order (their explicit form can be found in [7]), x i are independent three-dimensional variables and t is the time.…”

Section: Mathematical Models and Methods Used 21 Mechanical Modelsmentioning

confidence: 99%

Modelling of Dynamic Problems in Biomechanics

Petrov

Bolotskikh

Vasyukov

2011

Math. Model. Nat. Phenom.

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Numerical study of some dynamic problems of the mechanics of a deformable rigid body by the mesh-characteristic method

Cited by 40 publications

References 3 publications

Numerical study of the anisotropy of wave responses from a fractured reservoir using the grid-characteristic method

Numerical study of the anisotropy of wave responses from a fractured reservoir using the grid-characteristic method

Estimation of anisotropy of seismic response from fractured geological objects

Modelling of Dynamic Problems in Biomechanics

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