GRID-CHARACTERISTIC METHOD WITH IMPLICIT SCHEMES AND CONTACT CONDITIONS AT THE MATERIAL INTERFACE

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Resumo

The paper presents a modified grid-characteristic method for modeling the propagation of elastic waves in heterogeneous media with explicit material boundaries. The proposed approach is based on the use of implicit and explicit numerical solution schemes, which together ensure stability and accuracy at large time steps and small space steps in areas with elongated shapes. The correct formulation of contact conditions between materials was implemented both in the form of reflected and refracted waves, and by modifying the lines of the system of equations for the implicit scheme. Numerical experiments for one-dimensional and two-dimensional problems, including wave modeling in multilayer structures and glass composites, are presented. The convergence order has been estimated for various schemes. The results show the possibility of the developed method to provide high modeling accuracy and the ability to describe complex wave patterns in heterogeneous media.

Sobre autores

E. Pesnya

Moscow Institute of Physics and Technology

Email: pesnya.ea@phystech.edu
Dolgoprudny, Russia

I. Petrov

Moscow Institute of Physics and Technology; Innopolis University

Email: petrov@mipt.ru
Dolgoprudny, Russia; Innopolis, Russia

A. Favorskaya

Moscow Institute of Physics and Technology; Innopolis University

Email: aleanera@yandex.ru
Dolgoprudny, Russia; Innopolis, Russia

Bibliografia

  1. Wandowski T., Kudela P., Ostachowicz W.M. Numerical analysis of elastic wave mode conversion on discontinuities // Composite Structures. 2019. V. 215. P. 317–330.
  2. Farago I. Splitting methods and their application to the abstract Cauchy problems // Lecture Notes in Computer Science. 2005. V. 3401. P. 35–45.
  3. Pesnya E.A., Favorskaya A.V., Kozhemyachenko A.A. Implicit hybrid grid-characteristic method for modeling dynamic processes in acoustic medium // Lobachevskii Journal of Mathematics. 2022. V. 43.№4. P. 1032–1042.
  4. Wang Y., Tamma K., Maxam D., Xue T., Qin G. An overview of high-order implicit algorithms for first-/secondorder systems and novel explicit algorithm designs for first-order system representations // Archives of Computational Methods in Engineering. 2021. V. 28. P. 3593–3619 .
  5. Maier R., Peterseim D. Explicit computational wave propagation in micro-heterogeneous media // arXiv preprint. 2018. arXiv:1803.07898.
  6. Liu H., Luo Y. An explicit method to calculate implicit spatial finite differences // Geophysics. 2022. V. 87. № 2. P. T157–T168.
  7. Griswold A., Saye R. Modellingwave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods // Computer Methods in Applied Mechanics and Engineering. 2022. V. 395. Art. 114971.
  8. Petrov I.B., Favorskaya A.V. Computation of seismic resistance of an ice island by the grid-characteristic method on combined grids // Computational Mathematics and Mathematical Physics. 2021. V. 61.№8. P. 1339–1352.
  9. Kozhemyachenko A.A., Favorskaya A.V. Grid convergence analysis of grid-characteristic method on chimera meshes in ultrasonic nondestructive testing of railroad rail // Computational Mathematics and Mathematical Physics. 2023. V. 63.№10. P. 1886–1903.
  10. Golubev V.I. The grid-characteristic method for applied dynamic problems of fractured and anisotropic media // Proc. of GRID’2021 Conference. 2021.
  11. Pesnya E.A., Petrov I.B. Dynamic processes calculation in composites considering internal structure using the gridcharacteristic method // Lobachevskii Journal of Mathematics. 2024. V. 45.№1. P. 319–327.
  12. Nikitin I.S., Golubev V.I. Explicit–implicit schemes for calculating the dynamics of layered media with nonlinear conditions at contact boundaries // Journal of Siberian Federal University. 2021. V. 14.№6. P. 768–778.
  13. Golubev V.I., Nikitin I.S., Burago N.G., Golubeva Y.A. Explicit–implicit schemes for calculating the dynamics of elastoviscoplastic media with a short relaxation time // Differential Equations. 2023. V. 59.№6. P. 822–832.
  14. Shevchenko A.V., Golubev V.I. Boundary and contact conditions of higher order of accuracy for grid-characteristic schemes in acoustic problems // Computational Mathematics and Mathematical Physics. 2023. V. 63. № 10. P. 1760–1772.
  15. Liu Q.Q., Zhuang M., Zhan W., Shi L., Liu Q.H. A hybrid implicit-explicit discontinuous Galerkin spectral element time domain method for computational elastodynamics // Geophysical Journal International. 2023. V. 234. № 3. P. 1855–1869.
  16. Suarez-Carreno F., Rosales-Romero L. Convergency and stability of explicit and implicit schemes in the simulation of the heat equation // Applied Sciences. 2021. V. 11.№10. Art. 4468.
  17. Favorskaya A.V., Petrov I.B., Kozhemyachenko A.A. Grid-characteristic method combined with discontinuous Galerkin method for simulation of wave propagation through linear elastic media in three-dimensional case // Computational Mathematics and Mathematical Physics. 2025. V. 65.№2. P. 403–415.
  18. Deucher R.H., Tchelepi H.A. High-resolution adaptive implicit method for reactive transport in heterogeneous porous media // Journal of Computational Physics. 2022. V. 466. Art. 111391.
  19. Guseva E.K., Golubev V.I., Petrov I.B. Numerical computation of methane migration effect on seismic survey results in permafrost zones // Computational Mathematics and Mathematical Physics. 2024. V. 64.№9. P. 2085–2093.
  20. Buwalda F.J., De Goede E., Knepfle M., Vuik C. Comparison of an explicit and implicit time integration method on GPUs for shallow water flows on structured grids // Water. 2023. V. 15.№6. Art. 1165.

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