We present an efficient and accurate immersed boundary (IB) finite element (FE) solver for numerically solving incompressible Navier-Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in the vasculature system). IB methods are computationally costly for internal flows, mainly due to the large percentage of grid points that lie outside the flow domain. In this study, we apply a local refinement strategy, along with a domain reduction approach in order to reduce the grid that covers the flow domain and increase the percentage of the grid nodes that fall inside the flow domain. The proposed method utilizes an efficient and accurate FE solver with the incremental pressure correction scheme (IPCS), along with the boundary condition enforced IB method to numerically solve the transient, incompressible Navier-Stokes flow equations. We verify the accuracy of the numerical method using the analytical solution for Poiseuille flow in a cylinder. We further examine the accuracy and applicability of the proposed method by considering flow within complex geometries, such as blood flow in aneurysmal vessels and the aorta, flow configurations which would otherwise be extremely difficult to solve by most IB methods. Our method offers high accuracy, as demonstrated by the verification examples, and high efficiency, as demonstrated through the solution of blood flow within complex geometry on an off-the-shelf laptop computer.

Magnetic drug targeting (MDT) is a noninvasive method for the medical treatment of various diseases of the cardiovascular system. Biocompatible magnetic nanoparticles loaded with medicinal drugs are carried to a tissue target in the human body (in vivo) under the applied magnetic field. The present study examines the MDT technique in various microchannels geometries by adopting the principles of biofluid dynamics (BFD). The blood flow is considered as laminar, pulsatile and the blood as an incompressible and non-Newtonian fluid. A two-phase model is adopted to resolve the blood flow and the motion of magnetic nanoparticles (MNPs). The numerical results are obtained by utilizing a meshless point collocation method (MPCM) alongside with the moving least squares (MLS) approximation. The numerical results are verified by comparing with published numerical results. We investigate the effect of crucial parameters of MDT, including (1) the volume fraction of nanoparticles, (2) the location of the magnetic field, (3) the strength of the magnetic field and its gradient, (4) the way that MNPs approach the targeted area, and (5) the bifurcation angle of the vessel.

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