Abstract:
We study the grid-characteristic methods for solving hyperbolic systems using a high order interpolation on unstructured tetrahedral and triangular grids for approximation. We consider the interpolation with orders from the first to the fifth included. Also, one-dimensional finite difference schemes appropriate for the considered methods are given. We study these schemes in terms of stability. The grid-characteristic method on unstructured triangular and tetrahedral grids are successfully used for solving the seismic prospecting problems, including, seismic prospecting in the conditions of the Arctic shelf and permafrost, as well as for solving seismic problems, problems of dynamic deformation and destruction, studying anisotropic composite materials.
Key words:
grid-characteristic method, numerical simulation, unstructured grids, high order interpolation.
Citation:
A. V. Favorskaya, I. B. Petrov, “The study of increased order grid-characteristic methods on unstructured grids”, Sib. Zh. Vychisl. Mat., 19:2 (2016), 223–233; Num. Anal. Appl., 9:2 (2016), 171–178
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\jour Num. Anal. Appl.
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\pages 171--178
\crossref{https://doi.org/10.1134/S1995423916020087}
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Linking options:
https://www.mathnet.ru/eng/sjvm614
https://www.mathnet.ru/eng/sjvm/v19/i2/p223
This publication is cited in the following 16 articles:
I. V. Popov, “Modeling wave processes in elastic media based on conservative difference schemes”, Math. Models Comput. Simul., 13:6 (2021), 1160–1171
I. B. Petrov, A. V. Favorskaya, “Computation of seismic resistance of an ice island by the grid-characteristic method on combined grids”, Comput. Math. Math. Phys., 61:8 (2021), 1339–1352
A. V. Favorskaya, N. I. Khokhlov, I. B. Petrov, “Grid-characteristic method on joint structured regular and curved grids for modeling coupled elastic and acoustic wave phenomena in objects of complex shape”, Lobachevskii J. Math., 41:4, SI (2020), 512–525
Alena V. Favorskaya, Vasily I. Golubev, “Elastic and acoustic approximations for solving direct problems of human head ultrasonic study”, Procedia Computer Science, 176 (2020), 2566
Katerina Beklemysheva, Alexey Ermakov, Alena Favorskaya, “Numerical simulation of cone object destruction under a short high-energy pulse”, Procedia Computer Science, 159 (2019), 1095
A. V. Favorskaya, “Investigation the material properties of a plate by laser ultrasound using the analysis of multiple waves”, Computer Research and Modeling, 11:4 (2019), 653–673
Polina V. Stognii, Nikolay I. Khokhlov, Smart Innovation, Systems and Technologies, 133, Smart Modeling for Engineering Systems, 2019, 156
A. V. Favorskaya, M. S. Zhdanov, N. I. Khokhlov, I. B. Petrov, “Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid-characteristic method”, Geophys. Prospect., 66:8 (2018), 1485–1502
A. V. Favorskaya, S. V. Kabisov, I. B. Petrov, “Modeling of ultrasonic waves in fractured rails with an explicit approach”, Dokl. Math., 98:1 (2018), 401–404
A. V. Favorskaya, I. B. Petrov, “Theory and practice of wave processes modelling”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag Berlin, 2018, 1–6
A. V. Favorskaya, “Interpolation on unstructured tetrahedral grids”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag Berlin, 2018, 45–73
A. V. Favorskaya, I. B. Petrov, “Grid-characteristic method”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag Berlin, 2018, 117–160
A. V. Favorskaya, M. S. Zhdanov, “Migration of elastic fields based on Kirchhoff and Rayleigh integrals”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag Berlin, 2018, 241–265
Alena Favorskaya, “The use of multiple waves to obtain information on an underlying geological structure”, Procedia Computer Science, 126 (2018), 1110
A. V. Favorskaya, I. B. Petrov, “The use of full-wave numerical simulation for the investigation of fractured zones”, Math. Models Comput. Simul., 11:4 (2019), 518–530
A. Favorskaya, I. Petrov, A. Grinevskiy, “Numerical simulation of fracturing in geological medium”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, eds. C. ZanniMerk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1216–1224
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