Geodesic
Finite difference schemes for modelling the propagation of axisymmetric elastic longitudinal waves
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 644-654

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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.
Keywords: elastic medium, cylindrical waves, splitting method, finite difference scheme, monotonicity, dissipativity, parallel computing. 
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     author = {Vladimir M. Sadovskii and Oxana V. Sadovskaya and Evgenii A. Efimov},
     title = {Finite difference schemes for modelling the propagation of axisymmetric elastic longitudinal waves},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {644--654},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a11/}
}
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Vladimir M. Sadovskii; Oxana V. Sadovskaya; Evgenii A. Efimov. Finite difference schemes for modelling the propagation of axisymmetric elastic longitudinal waves. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 644-654. http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a11/