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Diffuse interface approach to modeling wavefields in a saturated porous medium

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  • Galina, Reshetova
  • Evgeniy, Romenski

Abstract

We present a model and numerical technique method for simulation a small-amplitude wave propagation in the fluid-saturated porous medium in regions with different porosity, including domains with pure fluid and pure solid. The governing equations are derived from the general hyperbolic thermodynamically compatible model of compressible fluid flow in a deformed porous medium. The resulting linear partial differential equations (PDE) form the symmetric hyperbolic system written for velocities, relative velocities, pressure and shear stress, which ensures application of a high order finite difference scheme on a staggered grid. A diffuse interface approach is applied to simulate wavefields in regions with interfaces between media with different porosity, including pure phases. The latter allows computations with the use of a single PDE system on rectangular grids without cumbersome interface tracking. Numerical experiments confirming the efficiency of the proposed approach are presented.

Suggested Citation

  • Galina, Reshetova & Evgeniy, Romenski, 2021. "Diffuse interface approach to modeling wavefields in a saturated porous medium," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    • Handle: RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300321000266
    DOI: 10.1016/j.amc.2021.125978
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