MBI Publications for Immersed Boundary Method (4)
E. Jung, S. Lim, S. Lee and W. Lee
Computational models of valveless pumping using the immersed boundary methodComputer Methods in Applied Mechanics and EngineeringVol. 197 No. Series 25-28 (2008) pp. 2329-2339
AbstractMathematical models of valveless pumping can be represented by either a closed loop system or an open tube system. In this paper, we present a three-dimensional model of valveless pumping in a closed loop system. We also present a two-dimensional model using an open elastic cylinder contained in a rigid tank. In both models, we take the periodic compress-and-release action at the asymmetric location of the soft tube and observe the existence of a net flow and the important features of valveless pumping that have been reported in the previous models or experiments. The innovative idea of this work is that we explain the existence of a net flow by introducing the concept of the signed area of the flow-pressure loop over one cycle, which represents the power in the system. The direction and the magnitude of a net flow can also be explained by the sign and the amount of power, which is work done on the fluid by the fluid pressure and the elastic wall over one period, respectively.
S. Lim, A. Ferent, X. Wang and C. Peskin
Dynamics of a closed rod with twist and bend in fluidSIAM Journal on Scientific ComputingVol. 31 No. 1 (2008) pp. 273-302
AbstractWe investigate the instability and subsequent dynamics of a closed rod with twist and bend in a viscous, incompressible fluid. A new version of the immersed boundary (IB) method is used in which the immersed boundary applies torque as well as force to the surrounding fluid and in which the equations of motion of the immersed boundary involve the local angular velocity as well as the local linear velocity of the fluid. An important feature of the IB method in this context is that self-crossing of the rod is automatically avoided because the rod moves in a continuous (interpolated) velocity field. A rod with a uniformly distributed twist that has been slightly perturbed away from its circular equilibrium configuration is used as an initial condition, with the fluid initially at rest. If the twist in the rod is sufficiently small, the rod simply returns to its circular equilibrium configuration, but for larger twists that equilibrium configuration becomes unstable, and the rod undergoes large excursions before relaxing to a stable coiled configuration.
Y. Kim, S. Lim, S. Raman, O. Simonetti and A. Friedman
Blood flow in a compliant vessel by the immersed boundary methodAnnals of Biomedical EngineeringVol. 37 No. 5 (2009) pp. 927-942
AbstractIn this paper we develop a computational approach to analyze hemodynamics in the aorta; this may serve as a useful tool in the development of noninvasive methods to detect early onset of diseases such as aneurysms and stenosis in major blood vessels. We introduce a mathematical model which describes the interaction of blood flow with the aortic wall; this model is based on the immersed boundary method. A two-dimensional vessel model is constructed, the velocity at the inlet is prescribed based on the information from the Magnetic Resonance Imaging data measured in the aorta of a healthy subject, and the velocity at the outlet is prescribed by driving the pressure level reproduced from the literature. The mathematical model is validated by comparing with well-known solutions of the viscous incompressible Navier√Ę‚?¨‚??Stokes equations, i.e., Womersley flow. The hysteresis behavior in the pressure√Ę‚?¨‚??diameter relation is observed when the viscoelastic material property of the arterial wall is taken into consideration. Five different shapes of aortic wall are considered for comparison of the flow patterns inside the aorta: one for the normal aorta, two for the dilated aorta, and two for the constrictive aorta.
S. Lim and E. Jung
A three-dimensional model of a closed valveless pup system immersed in a viscous fluidSIAM J. Appl. Math.Vol. 70 No. 6 (2010) pp. 1999-2010
Abstract: We present a three-dimensional model of flow driven by pumping without valves (valveless pumping) in a closed loop system in which the closed loop of tubing is immersed in an incompressible viscous fluid. This closed tube consists of two parts, an open cylindrical soft tube and an open rigid tube, smoothly connected to one another. At an asymmetric location of the soft tube, a periodic compress-and-release action with a time delay between actions is taken to create a net flow. Numerical results show that the magnitude of average net flow and flow direction inside the tube depend on the pumping frequency, the amplitude of periodic forcing, the compression duration, the length of the soft tube, and the elastic properties of the tube. Fluid viscosity is also found to influence net flow. The immersed boundary method is used to investigate the interaction between the tube and the fluid and to study the valveless pumping mechanism. (A correction to the this article has been appended at the end of the pdf file.)