THREE-DIMENSIONAL GRID CHARACTERISTIC SCHEMES OF HIGH ORDER OF APPROXIMATION

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

This paper examines the process of the seismic wave propagation in a full three-dimensional case. To describe the stress-strain state of a geological medium during seismic exploration, acoustic and linear elastic models are widely used in practice. The governing systems of partial differential equations of both models are linear hyperbolic. To construct a computational algorithm for solving them, a grid-characteristic approach can be used. In this case, an important question in multidimensional problems relates to the use of the splitting method. However, despite the use of extended spatial stencils to solve the resulting onedimensional problems, it is not possible to preserve the achieved approximation order when constructing the final three-dimensional scheme. In this paper, we propose an approach based on the multi-stage operator splitting schemes, which made it possible to construct a three-dimensional grid-characteristic scheme of the third approximation order. Given verification problems were solved numerically.

Авторлар туралы

I. Petrov

Moscow Institute of Physics and Technology (National Research University)

Email: petrov@mipt.ru
Corresponding Member of the RAS Dolgoprudny, Moscow Region, Russia

V. Golubev

Moscow Institute of Physics and Technology (National Research University)

Email: w.golubev@mail.ru
Dolgoprudny, Moscow Region, Russia

A. Shevchenko

Moscow Institute of Physics and Technology (National Research University); Ishlinsky Institute for Problems in Mechanics RAS

Email: alexshevchenko@phystech.edu
Dolgoprudny, Moscow Region, Russia; Moscow, Russia

A. Sharma

IPS Academy, Institute of Engineering and Science

Email: amitsharma@ipsacademy.org
Indore, India

Әдебиет тізімі

  1. Moczo P., Kristek J., Kristekova M., Valovčan J., Galis M., Gregor D. Material Interface in the Finite-Difference Modeling: A Fundamental View. Bulletin of the Seismological Society of America. 2022. V. 113. № 1. P. 281–296.
  2. Duru K., Rannabauer L., Gabriel A.-A., Ling O., Igel H., Bader M. A stable discontinuous Galerkin method for linear elastodynamics in 3D geometrically complex elastic solids using physics based numerical fluxes. Computer Methods in Applied Mechanics and Engineering. 2022. V. 389. P. 114386.
  3. Vogl C., Leveque R. A High-Resolution Finite Volume Seismic Model to Generate Seafloor Deformation for Tsunami Modeling. Journal of Scientific Computing. 2017. V. 73. P. 1204–1215.
  4. Магомедов К. М., Холодов А. С. Сеточнохарактеристические численные методы. М.: Наука, 2018. 287 с.
  5. Dovgilovich L., Sofronov I. High-accuracy finitedifference schemes for solving elastodynamic problems in curvilinear coordinates within multiblock approach. Appl. Numer. Math. 2015. V. 93. P. 176–194.
  6. Nishikawa H., Van Leer B. Towards high-order boundary procedures for finite-volume and finitedifference schemes. 2023. https://doi.org/10.2514/6.2023-1605
  7. Khokhlov N. I., Favorskaya A., Furgailo V. GridCharacteristic Method on Overlapping Curvilinear Meshes for Modeling Elastic Waves Scattering on Geological Fractures. Minerals. 2022. V. 12. P. 1597.
  8. Петров И. Б., Голубев В. И., Петрухин В. Ю., Никитин И. С. Моделирование сейсмических волн в анизотропных средах. Доклады Российской академии наук. Математика, информатика, процессы управления. 2021. Т. 498. № 1. С. 59–64.
  9. Петров И. Б., Голубев В. И., Шевченко А. В. О задаче акустической диагностики прискважинной зоны. Доклады Российской академии наук. Математика, информатика, процессы управления. 2020. T. 492. № 1. С. 92–96.
  10. Голубев В. И., Никитин И. С., Бураго Н. Г., Голубева Ю. А. Явно-неявные схемы расчета динамики упруговязкопластических сред с малым временем релаксации. Дифференциальные уравнения. 2023. Т. 59. № 1. С. 1–11.
  11. Головизнин В. М., Соловьев А. В. Дисперсионные и диссипативные характеристики разностных схем для уравнений в частных производных гиперболического типа. М.: МАКС Пресс, 2018, 198 с.
  12. Головизнин В. М., Соловьев А. В. Диссипативные и дисперсионные свойства разностных схем для линейного уравнения переноса на меташаблоне 4 × 3. Матем. моделирование, 33:6 (2021), 45–58; Math. Models Comput. Simul., 14:1 (2022), 28–37.
  13. Trotter H. F. Approximation of semi-groups of operators. Pac. J. Math. 1958. V. 8. No. 4. P. 887–919.
  14. Godunov S. K. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mat. Sb. 1959. V. 89. № 3. P. 271–306.
  15. Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 1968. V. 5. P. 506–517.
  16. Ruth R. D. A canonical integration technique. IEEE Trans. Nuclear Sci. 1983. V. 30. P. 2669–2671.
  17. Cervi J., Spiteri R. High-Order Operator Splitting for the Bidomain and Monodomain Models. SIAM Journal on Scientific Computing. 2018. V. 40. №. 2. P. A769–A786.
  18. Cervi J., Spiteri R. A comparison of fourth-order operator splitting methods for cardiac simulations. Applied Numerical Mathematics. 2019. V. 145. P. 227–235.
  19. Golubev V. I., Shevchenko A. V., Petrov I. B. Raising convergence order of grid-characteristic schemes for 2D linear elasticity problems using operator splitting. Computer Research and Modeling. 2022. V. 14. № 4. P. 899–910.
  20. Sedov L. I. Course in Continuum Mechanics (Nauka, Moscow, 1970; Wolters-Noordhoff, Groningen, 1971), V. 1.
  21. Rusanov V. V. Difference schemes of the third order of accuracy for the forward calculation of discontinuous solutions. Dokl. Akad. Nauk SSSR. 1986. V. 180. № 6. P. 1303–1305.
  22. Kholodov A. S. The construction of difference schemes of increased order of accuracy for equations of hyperbolic type. USSR Computational Mathematics and Mathematical Physics. 1980. V. 20. № 6. P. 234–253.
  23. Auzinger W., Koch O., Thalhammer M. Defectbased local error estimators for high-order splitting methods involving three linear operators. Numer Algor. 2015. V. 70. P. 61–91.
  24. Петров И. Б., Голубев В. И., Шевченко А. В., Никитин И. С. Об аппроксимации граничных условий повышенного порядка в сеточнохарактеристических схемах. Доклады Российской академии наук. Математика, информатика, процессы управления. 2023. T. 514. № 1. С. 52–58.

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