The form for representing the equation of motion for porous media in terms of velocities, stresses, and pressure as a symmetric hyperbolic Friedrechs system has been obtained. A two-dimensional initial- boundary value problem in a half-space is considered, the excitation source is a point source. For its numerical solution, an explicit predictor-corrector scheme is used. A series of numerical calculations for a test model of media is presented.
1. Carcione J.M., Morency C. and Santos J.E. Computational poroelasticity – a review. Geophysics. Vol. 75, Issue 5, A229–A243 (2010).
3. Zhu X. and McMechan A. Numerical simulation of seismic responses of poroelastic reservoirs using Biot’s theory. Geophysics. Vol. 56, Issue 3, 328–339 (1991).
4. Dai N., Vafidis A. and Kanasewich E. Wave propagation in heterogeneous, porous media: a velocity-stress, finite-difference method. Geophysics. Vol. 60, 327–340. (1995).
5. Zeng Y. and Liu Q. The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media: Geophysics. Vol. 66, Issue 4, 1258–1266 (2001).
6. Sheen D.H., Tuncay K., Baag C. and Ortoleva P. Parallel implementation of a velocity-stress staggered-grid finite-difference method for 2-d poroelastic wave propagation. Computers and Geo-sciences. Vol. 32, 1182–1191 (2006).
7. Imomnazarov Kh.Kh., Mikhailov A.A. Using Laguerre spectral method for solving a linear two-dimensional dynamic problem for porous media. Siberian Journal of Industrial Mathematics. Issue 11, 86–95 (in Russian) (2008).
8. Moradi S. and Don C. Lawton Velocity-stress finite-difference modeling of poroelastic wave propagation. CREWES Research Report. Vol. 25, 1–10 (2013).
9. Dupuy B., De Barros L., Garambois S. and Virieux J. Wave propagation in heterogeneous porous media formulated in the frequency-space domain using a discontinuous Galerkin method. Geophysics. Vol. 76, Issue 4, 13–28(2011).
10. Lemoine G.I., Ou M.Y. and LeVeque R.J. High-resolution finite volume modeling of wave propagation in orthotropic poroelastic media. SIAM Journal on Scientific Computing. Vol. 35, Issue 1, B176–B206 (2013).
11. Soboleva O.N., Kurochkina E.P. Flow through Anisotropic Porous Medium with Multiscale Log-Normal Conductivity. Journal of Porous Media. Vol. 13, Issue 2, 171–182 (2010).
12. Soboleva O.N. Modeling of Propagation of Antiplane Acoustic Waves in Multiscale Media with Lognormal Distribution of Parameters. Journal of computational acoustics. Vol. 25, 6–14 (2017).
13. Frenkel Ya.I. On the theory of seismic and seismoelectric phenomena in a moist soil. Journal of Physics. USSR. Vol. 8, 230–241 (1944).
14. Biot M.A. Theory of propagation of elastic waves in fluid-saturated porous solid I. low-frequincy range. The Journal of the Acoustical Society of America. Vol. 28, 168–178 (1956).
15. Imomnazarov Kh.Kh. Some remarks on the system of Bio equations. Reports of the Russian Academy of Sciences. Vol. 373, Issue 4, 536–537 (2000).
16. Imomnazarov Kh.Kh. Some remarks on the Biot system of equations describing wave propagation in a porous medium. Applied Mathematics Letters. Vol. 13, Issue 3, 33–35 (2000).
17. Dorovsky V.N., Perepechko Yu.V., Romensky E.I. Wave processes in saturated porous elastically deformable media. Combustion and Explosion Physics - 1993. Issue 1, 100–111 (1993).
18. Blokhin A.M., Dorovsky V.N. Mathematical Modeling Problems in the theory of multi-velocity continuum. Novosibirsk. 183 p. (1994).
19. Jabborov N.M., Imomnazarov H.Kh. Some initial boundary value problems in the mechanics of two-speed media. Tashkent. 212 p. (2012).
20. Imomnazarov Kh.Kh., Kholmurodov A.E. Modeling and investigation of direct and inverse dynamic problems of poroelasticity. University, Tashkent. 120 p. (in Russian) (2017).
21. Godunov S.K. Equations of Mathematical Physics (2nd ed.). Moscow: Science. 391 p. (1979).
"The symmetric form of a poroelasticity system in terms of velocities, stresses and pressure,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 3
, Article 7.
Available at: https://uzjournals.edu.uz/mns_nuu/vol3/iss2/7