توسعه يك مدل محيط متخلخل مناسب براي شبيه‌سازي عددي جريان خون درون لوبول‌هاي كبدي به منظور در نظر گرفتن مويرگ‌هاي خوني

The numerical simulation of blood flow through liver lobules is important from different points of view such as drug delivery. Each liver lobule can be considered as a six-sided shape porous medium, which is surrounded by a set of blood veins. In addition, there exists, some flow channels inside this porous medium, which are called sinosoids. As a result, each liver lobule can be considered as a channelized porous medium. Fluid flow through channelized porous medium can be simulated by using an appropriate numerical method in such a way that the governing equations related to the matrix of the medium an‎d those of the flow channels are simuletentously solved. In this approach, which is called the direct model, the Navier-Stokes equation inside the flow channels alogn with the Brinkman equations in porous regions are solved. Although the direct approach provides accurate results, it is generallycomputationally expensive. This issue becomes more challengious in the case of fluid flow through complicated an‎d three-dimensional geometries. In this thesis, a mathematical-numerical model, which is named porou medium model, has been suggested in order to provide acceptable results at low computational costs for problems associated with fluid flow in channelized porous medium. Compared to the direct approach, the suggested model epmpys the Darcy’s law enhanced with proper absolute permeability fields, rather than the set of Navier-Stokes-Brinkman equations, resulting in a reduction in total computational costs. In this method, first, a steady-state problem in the coisdered domain is defined an‎d solved an‎d a coarse-scaele permeability value is computed by using the obtained solution. In order to achieve a permeability field at the original scale, a prolongation oprator named wall distance function is employed. This wall distance function is calculated inside the flow channels an‎d used to compute the required permeability distribution inside these channles. By using the proposed model, blood flow inside the liver obuls is numerically simulated an‎d its results an‎d performance are compared to those of the reference (direct) model. Numerical results of two- an‎d three-dimensional test cases indicate that the maximum error in the velocity field obtained by the porous medium model is less than 14%, while the CPU time ratio of the porous medium model an‎d the reference model is about 0.5. According to the presented results, one can consider the porous medium model as an effective an‎d computationally efficient tool, when compared to the reference model.

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