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Семинар по проект "Математическо моделиране на спрегнати процеси в еднофазни нееднородни и многофазни среди" утре, 15.12.2011, от 11.00. На семинара доклад ще има д-р Петър Попов от Институтa по информационни и комуникационни технологии:

MULTISCALE MODELING AND SIMULATION OF FLUID FLOWS IN HIGHLY DEFORMABLE POROUS MEDIA

In this work a new class of methods for upscaling fluid-structure interaction problems from the pore-level to a macroscale is proposed. We consider a fully coupled fluid-structure interaction problem for stokes fluid and an elastic solid at the pore-level. The solid, due to coupling with the fluid, material nonlinearities, as well as macroscopic boundary conditions, can deform enough so that the pore-space is altered significantly. As a result, macroscopic properties such as the permeability of the porous media become nonlinearly dependent on the fine-scale displacements. Therefore, classical upscaled models, such as Biot's equations, can no longer be applied. We propose a series of numerical upscaling models which couple this fine-scale FSI problem to a nonlinear elliptic equation for the averaged pressure and displacements at the coase scale. The proposed multiscale methods correclty transfer the appropriate physics from the fine to the coarse scale. Moreoever they are intrinsically parallelizable on a wide variety of computer architectures. Next, the special case of flow past elastic obstacles is further studied. In that particular case the macroscopic equations involve only a nonlinear Darcy law for the averaged pressure. As a result the multiscale method can be analyzed, and, under certain assumptions, we prove that it converges to the fine-scale solution. Several numerical examples which demonstrate the method are also presented.