Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods

Biryukov, Vladimir Aleksandrovich; Miryakha, V. A.; Petrov, I. B.; Хохлов, Н. И.

doi:10.1134/s0965542516060087

Cited by 29 publications

(12 citation statements)

References 28 publications

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“…The discontinuous Galerkin method was proposed in the seventies of the previous century in [42] and constant development of the method has been observed since the time, see [9,13,19,34,44] and its application to many problems, such as analysing plates and shell [17,36], elastic wave propagation [6,7] or fluid floats [3,32]. The present paper constitutes another step towards developing the DG method, with particular attention to the DGFD method.…”

Section: Introductionmentioning

confidence: 99%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

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The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

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Section: Introductionmentioning

confidence: 99%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

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“…The examples of comparison between GCM and other numerical methods for more complicated models can be found in Biryukov et al . ().…”

Section: Numerical Comparison Of the Grid‐characteristic Methods With mentioning

confidence: 97%

“…Our test models were relatively simple in order to compare the GCM with the analytical solutions. The examples of comparison between GCM and other numerical methods for more complicated models can be found in Biryukov et al (2016).…”

Section: N U M E R I C a L C O M P A R I S O N O F T H E G R I D -C Hmentioning

confidence: 99%

“…The comparison between GCM approach and the other forward modelling techniques was discussed in Biryukov et al . ().…”

Section: Introductionmentioning

confidence: 97%

“…We should note that the method can be used to model the wave propagation in lossy media as well; however, in this paper we will consider the non-dispersive media only. The comparison between GCM approach and the other forward modelling techniques was discussed in Biryukov et al (2016).…”

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confidence: 99%

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Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

Favorskaya

Zhdanov

Хохлов

et al. 2018

Geophysical Prospecting

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This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.

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Effects of heat transfer on MHD suction–injection model of viscous fluid flow through differential transformation and Bernoulli wavelet techniques

Raghunatha

Vinod

2023

Heat Trans

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In this study, a numerical solution of the velocity and heat transfer on the magnetohydrodynamic suction–injection model of viscous fluid flow has been studied. We use the differential transformation method and Bernoulli wavelet method to solve the highly nonlinear governing equations; applying appropriate similarity transformations and reducing governing equations to highly nonlinear coupled ordinary differential equations. The objective of this analysis is to determine how the suction parameter, Hartmann number, squeeze number, thermophoresis parameter, and Prandtl number affect the velocity and temperature profiles. When the current findings are compared with those that have already been published in the literature, confident suppositions are made, and it is discovered that there is considerable agreement. Graphs have been used to discuss the influence of nondimensional characteristics on velocity and temperature.

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Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods

Cited by 29 publications

References 28 publications

Very high order discontinuous Galerkin method in elliptic problems

Very high order discontinuous Galerkin method in elliptic problems

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through differential transformation and Bernoulli wavelet techniques

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