Study Of The Blood Flows By Lattice Boltzmann Method

Since it was first proposed in 1988, the lattice Boltzmann method (LBM) has attracted much attention. Now, LBM has been accepted as an alternate hydrodynamic computational method, and its accuracy and robustness has been broadly confirmed. The applications include the numerical simulations of turbulent flows , two-phase flows, reaction-diffusion processes, granular and suspended particles. LBM is a discrete statistical model, and the information is transported locally during the computational process. This model is especially suitable for parallel computation on PC-cluster and even Internet Grid computing, because of the weak correlation of the program between the nodes. Consequently, one can perform large-scale computation with relatively low cost by using of LBM. The blood system is a typical biological one with complex boundaries. In this article, we will present our primary study on blood flows with LBM. Our progress includes the following three parts:(1) A method to evaluate the hydrodynamic force exerted ondeformable boundaries accurately was proposed. Because the velocity is discretized in LBM, and in order to decrease the computational complexity, the number of the discrete velocity is chosen as small as possible. For example, the velocity set has nine discrete velocities for the typical two-dimensional scheme D2Q9, and fifteen discrete velocities for three-dimensional one D3Q15. Wefound large errors of local hydrodynamic forces on small segments when the conventional method, i.e., the scheme based on the momentum-excahnge, was applied, while our method gives much accurate results. We have demonstrated the accuracy and robustness by numerical simulations of one particle sedimenting in fluid under gravity and moving in Poiseullie with the hydrodynamic forces evaluated by momentum-exchange and stress-integration respectively. Considerable errors were observed on the horizontal velocity of the settling particle under gravity by the momentum-exchange scheme while the results from our scheme are in excellent agreement with those from a finite element method. In Poiseuille flows, when the diameter ratio between the particle and the channel is greater than 0.2, the neutrally buoyant particle will migrate laterally away both from the wall and the centerline, and reach a certain lateral equilibrium position. This phenomenon is called Segre-Silberberg effect. The effect can be observed by our scheme while the particle always approaches the centeline for the momentum-exchange method.(2) The study of two-dimensional particle suspending through amodeled arterial stenosis by lattice Boltzmann simulation was proposed. The red blood cells (RBCs) are treated as rigid cylinders. The stenosis is created by adding two symmetric protuberances inside the vessel. The two protuberances are two semi-circles. When the clearance between two RBCs or the RBCs and the protuberances is less than one lattice, lubrication force is added. Our results show that there are two critical gaps bc0 and bc between the two protuberances.When the gap falls in the range bc0