---

In the present study, the motion and deformation of a red blood cell in the incompressible viscous flow is simulated using the lattice Boltzmann method combined with the immersed boundary method. The lattice Boltzmann method is used to solve the flow field, whereas the immersed boundary method is used to simulate the dynamics of the red blood cell. The red blood cell is considered as an elastic boundary immersed in the fluid domain. The main advantage of the lattice Boltzmann method is that it solves only an algebraic equation. In the immersed boundary method the fluid domain is descretized using a regular Eulerian grid, while the immersed boundary is represented in the Lagrangian coordinates. The Eulerian grid points would not necessarily coincide with the Lagrangian points. The fluid- immersed boundary interaction is modeled using an appropriate form of delta function. The effects of the no-slip condition are taken into account via a forcing term added to the Navier-Stokes Equations (here the lattice Boltzmann equation). In the present study, the tank-treading motion of a red blood cell in the viscous shear flow is simulated. The results are found to be in good agreement with the available experimental and numerical ones.

---

In this paper, the immersed boundary-lattice Boltzmann method has been employed to simulate non-Newtonian flow around curve boundaries. The pressure base lattice Boltzmann equations have been used to solve the Eulerian domain to estimate proper pressure gradient in the Poiseuille flow. In addition Immersed boundary method (IBM) utilizes a discrete set of force density is also used to represent the effect of boundary on flow domain. In addition to simulate the real physical dominate problem and study the right effects of non-Newtonian fluid properties, scaling parameters have been introduced to notice the relationship between physical and lattice variables. At First, the capability of present method is examined for simulating the power-law fluid flow around a confined circular cylinder and the results show good agreement with previous study. In the following, the power-law fluid flow around elliptical cylinder in a channel is investigated for three aspect ratios eta=1,1.5,2 and for 5

---

In this paper an improved immersed boundary method is used for simulating sinusoidal pitching oscillations of a symmetric airfoil. Immersed boundary methods because of using a fixed Cartsian grid are well suited for such moving boundary problems. Two test cases are used to validate the proposed method and the effects of oscillation frequency and amplitude on the flow field are investigated. Flow field vorticity and kinetic energy contours are reported in this paper. It is found that the deflected wake start to be appeared for Strouhal number more than 0.4 at a fixed pitching amplitude 0.71. A chaotic flow can be observed at oscillation amplitude 2.80, for a fixed Strouhal number, 0.22. Kintic energy contour shows that for Strouhal number 0.1, the airfoil performs work and transfers momentum to flow but the fluid energy loss due to the enlargement of flow separation zone decreases the momentum and kinetic energy behind the airfoil. Deficit momentum and kinetic energy behind the airfoil results in drag force increasing. By increasing the oscillation frequency and amplitude more momentum transfers to flow filed behind the airfoil which results in drag force decreasing.

---

In this paper 2D numerical model is used to study the effect of depth of airway surface liquid (ASL) on the muco-ciliary transport. An immersed boundary-lattice Boltzmann method is used to solve the momentum equation. In this study mucus is considered as the viscoelastic fluid an Oldroyd-B model is used as the constitutive equation of it. Immerse boundary method is used to study the propulsive effect of the cilia and also the effects of mucus– periciliary layer interface. Our results show that mean mucus velocity becomes maximized when the PCL depth is equal to the standard value of it i.e. 6 μm. By increasing or decreasing the depth of PCL or increasing the depth of mucus layer, mean mucus velocity reduces. Our study also shows that mucus viscosity ratio can play an important role on the muco-ciliary clearance. It means that by increasing the Newtonian part of mucus viscosity or by decreasing elastic contribution of the mucu, mean mucus velocity increases significantly. So reducing mucus velocity results from changing ASL depth can be completely modified by increasing the Newtonian part of mucus viscosity.

---

In the current study, the motion and deformation of an elastic membrane in a two-dimensional channel with and without a groove is simulated using a combined lattice Boltzmann-immersed boundary method. The lattice Boltzmann method is used to solve the fluid flow equations and the immersed boundary method is used to incorporate the fluid-membrane interaction. The elastic membrane is considered as a flexible boundary immersed in the flow domain. In the immersed boundary method, the membrane is represented in the Lagrangian coordinates while the fluid domain is discretized on a uniform fixed Eulerian grid. The interaction between the fluid and the membrane is modeled using Dirac delta function. The effects of no-slip boundary condition are enforced by addition of a forcing term to the lattice Boltzmann equation. Depending on the flow rate, the initial location and stiffness of the elastic membrane, the size of the groove, the membrane only rotates inside the groove or the flow moves it out of the groove. The results are presented in terms of flow velocity and pressure fields and membrane configuration at different times. Comparison between the present results and the available numerical and experimental ones shows good agreement between them.

---

The variation of wall shear stress (WSS) in the microvessels may damage the endothelial layers. It also changes the mass diffusion and sediment and may be considered as an important factor in the formation of the fatty plaques and causing heart disease. According to the importance of the issue, the aim of this paper is to study the effective parameters on the wall shear stress in microvessels. In this paper, the hybrid method, combined lattice Boltzmann and immersed boundary methods is used to simulate the red blood cell (RBC) motion in the plasma flow. It should be mentioned that red blood cell has significant effect on WSS, in this regard; the present results show that the blood rheological behavior has the important effect on WSS. The results also demonstrate the effect of stenosis severity and RBC location in different regions on wall shear stress and consequently causing heart, coronary disease. It should be noted that the presented results have been evaluated by previous numerical results for microvessels and the results show the ability of lattice Boltzmann method to simulate complex problems especially for modeling the deformable solid objects suspended in the fluid.

---

In this paper, motion of a flexible membrane and hydrodynamic interaction of multiple membranes in a microchannel are simulated by developing a computer code written in C. The membranes are considered as flexible boundaries immersed in the fluid. First a single biconcave shaped membrane with high rigidity is considered. Due to the rigidity of the membrane, it experiences tumbling motion and its vertical displacement becomes oscillatory. Then, the effects of initial position of a circular membrane on its deformation, vertical velocity and displacement are investigated. It was observed that as the initial location of the membrane approaches the channel’s central axis, its vertical displacement and velocity decreased, but its horizontal velocity component increased. Finally, the simultaneous motion of multiple membranes in a microchannel and their interaction with each other and with flow are evaluated. The membranes do not collide and hence the collision mechanism is not modeled. It was found that the upstream membrane experienced greatest deformation and the greatest force was exerted on it by the fluid on it. In addition, simultaneous presence of multiple membranes would result in a reduction in the flow velocity. The current numerical results have good agreement with the available valid numerical ones.

---

In this study, the hybrid Lattice Boltzmann - Finite difference - Immersed Boundary method has been used for investigation of problems with heat transfer. For this purpose, mass and momentum conservation equations are solved by the Immersed Boundary- Lattice Boltzmann method and finite difference method has been used for solving energy conservation equation. The effect of Immersed Boundary has been shown as force and external energy source term in equations and therefor flow and heat transfer around circular cylinder and also the effect of how to move cylinder in heating of fluid inside the cavity has been studied. for this purpose four kinds of movements: circular reciprocating, normal circular, diagonal amplitude and horizontal amplitude have been considered for the cylinder and in all cases, the changes of force coefficients and Nusselt number have been discussed. It has been showed that the circular reciprocating movement has more effect on heating of fluid inside the cavity, which indeed this movement reduces the time of fluid heating about 20 percent in comparison with normal circular and diagonal amplitude movement and approximately 37 percent in comparison with horizontal amplitude movement. In all of the studied problems, the efficiency of hybrid method has been proved.

---

In the present study, the interaction between Turgo turbine and water flow was simulated using 2D immersed boundary method. For this purpose, the available computer code was validated by some reliable results of numerical fluid - structure interaction study. Due to the complexity of modeling whole turbine and its details, only the part of Turgo turbine involving three blades was simulated and the obtained results of study was generalized to whole turbine. In order to increase the efficiency of Turgo turbine and obtain the optimal design criteria, different parameters of its components including the concavity of turbine blade, turbine water head, water discharge and the number of blades were investigated. The optimal value of each parameter is obtained according to efficiency values of turbine. Finally, the optimal values of mentioned parameters were used to propose some optimal pattern for the design of Turgo turbine. Also, the results of the analysis showed that the immersed boundary method despite having simple formulation and algorithm can be utilized to provide a reliable numerical solution to simulate interaction between the parts of turbine and water flow.

---

In this paper, a new immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate heat transfer problems with constant heat flux boundary condition. In this method, the no-slip boundary condition is enforced via implicit velocity correction method and the constant heat flux boundary condition is implied considering the difference between the desired heat flux and the estimated one. The velocity correction represented as a forcing term is added to Boltzmann equation and for temperature correction, a heat source/sink term is introduced to energy equation. Elimination of sophisticated grid generation process, simplicity and effectiveness while keeping the accuracy, are the main advantages of the proposed method. Using the developed method, natural convection around a hot circular cylinder with constant heat flux in an enclosure with cold walls has been simulated at Rayleigh numbers of 103–106. Moreover, effects of diagonal position of cylinder on the flow and heat transfer patterns and local Nusselt number distribution on the surface of cylinder and walls of enclosure have been investigated. The obtained results show that the location of maximum local Nusset number is extremely depended on the diagonal position of the cylinder. According to the results of this simulation, it can be said that the present method is able to imply accurately the constant heat flux boundary condition.

---

Atherosclerosis is responsible for almost 35% of annual deaths in developed countries. The disease could be due to an artery blockage by the interaction of an externally second phase (air bubbles, medicine carrying capsules) with a particle which is entered to the bloodstream. The effect of some most important affecting parameters on the blockage time of a microchannel due to the impact of a particle and a second moving second phase is investigated using lattice Boltzmann method and with programming Fortran90. The authors tried to mimic the physic of the flow of a small artery by generating the same geometry and changing geometrical and physical parameters. Lee and Lin Lattice Boltzmann multi-phase model is used beside the immersed boundary method. It is investigated the small changes in Capillary flow has no meaningful effect on the interaction of second phase and particle. But, the ratio of particle size to the channel width affects the blockage time in the microchannel. In fact, the blockage time will increase by an increase in the size of the particle. The initial size of the second phase to particle size ratio has the highest effect on the blockage time.


 

---

Numerical simulation of Eulerian fluid Lagrangian solid interaction incorporating H₂-O₂ mixture gas detonation plate forming by employing conservative element and solution element immersed boundary method in LS-DYNA software is proposed in this paper. The detonation mechanism includes 7 species and 16 reactions. The chemical reaction mechanism and detonation wave propagation of Eulerian solver and dynamic plastic response of mild steel thin plate of Lagrangian solver are discussed thoroughly. The Johnson-Cook phenomenological material model with failure criterion is used to provide accurate predictions of dynamic response and failure state of detonation loaded steel plates taking into account material strain-rate sensitivity and non-linearities. The 2D numerical model is validated by comparing the simulation results with experimental data for thickness strain. The simulated pressure-time history of combustion cylinder, von Mises stress and deflection pattern of plate are also represented. Furthermore, a series of numerical simulation was carried out to determine the effect of the magnitude of internal detonation pressure on plate, taking into account different combustion cylinder longitudinal capacities, pre-detonation pressures and ignition point locations. Results show that an increase of pre-detonation pressure is conducive to increase the value of maximum detonation pressure while decreasing the combustion duration. Moreover, combustion cylinder with higher longitudinal capacity is more powerful to deform the plate.