Simulation of 3D Wave Fields in Inhomogeneous Domain with Complex Topography Using the Lebedev Scheme
https://doi.org/10.25205/1818-7900-2020-18-4-66-85
Abstract
Numerical simulation is widely used in the study of wave fields in various media. One of the methods is to divide the domain of interest into elementary volumes and build a finite-difference scheme for numerical implementation. The work assumes that the domain can have a significant curvature of the surface, therefore, the technology of generating a mesh of curved cubes is used. This mesh provides good consistency between the discrete and physical models of the domain. A parallel algorithm is proposed for the numerical solution of a 3D linear system of elasticity theory, expressed via displacement velocities and stresses, using a curvilinear mesh and an explicit difference scheme based on the Lebedev scheme. The simulation results are presented. The calculations were carried out using the resources of the SSCC SB RAS.
About the Author
P. A. Titov
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Russian Federation
Russian Federation
References
1. Liseikin V. D. Grid generation method. 2nd ed. Berlin, Springer, 2010. ISBN 978-90-481-2912-6
2. Vaseva I. A., Liseikin V. D., Likhanova Yu. V., Morokov Yu. N. An elliptic method for construction of adaptive spatial grids. Russ. J. Numer. Anal. Math. Modelling, 2009, vol. 1, p. 65-78. DOI 10.1515/RJNAMM.2009.006
3. Лисейкин В. Д. Разностные сетки. Теория и приложения Новосибирск, 2014. 245 с.
4. Appelo D., Petersson N. A. A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Communications in computational physics 5, 2007, no. 1, p. 84-107.
5. Jose M. Carcione. The wave equation in generalized coordinates. Geophysics 59, 1994, no. 12, p. 1911-1919. DOI 10.1190/1.1443578
6. Титов П. А. Алгоритм и программа моделирования 2D-волновых полей в областях с криволинейной свободной поверхностью // Материалы конференции “Научный сервис в сети Интернет - 2014”. Новороссийск, Абрау-Дюрсо, 2014. C. 446-455.
7. Титов П. А. Моделирование упругих волн в средах со сложной топографией свободной поверхности // Вестник НГУ. Серия: Информационные технологии. 2018. Т. 16, № 4. С. 153-166.
8. Titov P. A technology of modeling of elastic waves propagation in media with complex 3D geometry of the surface with the aid of high performance cluster. Russian Supercomputing Days, Proc., 2016, p. 1020-1031.
9. Titov P. The Simulation of 3D Wave Fields in Complex Topography Media. In: Russian Supercomputing Days, CCIS 1129, 2019, p. 451-462. DOI 10.1007/978-3-030-36592-9_37
10. Vishnevsky D., Lisitsa V., Tcheverda V., Reshetova G. Numerical study of the interface errors of finite-difference simulations of seismic waves. Geophysics, 2014, vo. 79 (4), p. 219-232. DOI 10.1190/geo2013-0299.1
11. Vishnevsky D., Lisitsa V. Lebedev scheme for numerical simulation of wave propagation in 3D anisotropic elasticity. Geophysical Prospecting 58, 2010, p. 619-635. DOI 10.1111/j.1365-2478.2009.00862.x
12. William Gropp, Steven Huss-Lederman et al. MPI - The complete reference. Cambridge, Massachusetts, MIT Press, 1998, vol. 2, 205 p.
13. Glinskii B. M., Karavaev D. A., Kovalevsky V. V., Martynov V. N. Numerical modeling and experimental research of the «Karabetov Mountain» mud volcano by vibroseismic methods. Num. Meth. Prog., 2010, vol. 11 (1), p. 95-104.
14. Collino F., Tsogka C. Application of the Perfectly Matched Absorbing Layer Model to the Linear Elastodynamic Problem in Anisotropic Heterogeneous Media. Geophysics 66, 2001, p. 294-307. DOI 10.1190/1.1444908
Review
For citations:
Titov P.A. Simulation of 3D Wave Fields in Inhomogeneous Domain with Complex Topography Using the Lebedev Scheme. Vestnik NSU. Series: Information Technologies. 2020;18(4):66-85. (In Russ.) https://doi.org/10.25205/1818-7900-2020-18-4-66-85
Views:
73
Email this article 