This article is cited in 1 scientific paper (total in 1 paper)
Finite difference schemes for modelling the propagation of axisymmetric elastic longitudinal waves
Vladimir M. Sadovskii, Oxana V. Sadovskaya, Evgenii A. Efimov
Institute of Computational Modeling SB RAS, Krasnoyarsk, Russian Federation
An efficient finite difference shock-capturing scheme for the solution of direct seismic problems is constructed. Problem formulation is based on equations of the dynamics of elastic medium with axial symmetry. When implementating the scheme on multiprocessor computing systems, the two-cyclic splitting method with respect to spatial variables is used. One-dimensional systems of equations that arise in the context of splitting procedure are represented as subsystems for longitudinal, transverse and torsional waves. The case of longitudinal waves is considered in this paper. The results of simulations with the use of explicit grid-characteristic schemes and implicit schemes of the "predictor–corrector" type with controllable dissipation of energy are compared with exact solutions that describe propagation of monochromatic waves.
elastic medium, cylindrical waves, splitting method, finite difference scheme, monotonicity, dissipativity, parallel computing.
|Ministry of Science and Higher Education of the Russian Federation
|This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075-02-2020-1631).
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Received in revised form: 11.07.2020
Vladimir M. Sadovskii, Oxana V. Sadovskaya, Evgenii A. Efimov, “Finite difference schemes for modelling the propagation of axisymmetric elastic longitudinal waves”, J. Sib. Fed. Univ. Math. Phys., 13:5 (2020), 644–654
Citation in format AMSBIB
\by Vladimir~M.~Sadovskii, Oxana~V.~Sadovskaya, Evgenii~A.~Efimov
\paper Finite difference schemes for modelling the propagation of axisymmetric elastic longitudinal waves
\jour J. Sib. Fed. Univ. Math. Phys.
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Efimov E.A., Sadovskii V.M., Sadovskaya V O., “Mathematical Modeling of the Impact of a Pulse Seismic Source on Geological Media”, AIP Conference Proceedings, 2302, ed. Todorov M., Amer Inst Physics, 2020, 120002
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