Browsing by Subject "immersed boundary method"

Now showing 1 - 4 of 4
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    Accuracy improvement of the immersed boundary–lattice Boltzmann coupling scheme by iterative force correction
    (Elsevier, 2016-01) Zhang, Chunze; Cheng, Yongguang; Zhu, Luoding; Wu, Jiayang; Department of Mathematical Sciences, School of Science
    The non-slip boundary condition at solid walls cannot be accurately achieved by the conventional immersed boundary–lattice Boltzmann (IB–LB) coupling schemes due to insufficient interpolation accuracy. To solve this problem, an iterative force correction procedure for the IB–LB coupling scheme is proposed. Cheng’s external forcing term in the LB equation is selected to properly incorporate the present and the next time step effects. The unknown IB force and the corresponding force on fluid at the next time step are calculated by iterative correction, based on the known immersed boundary speed, flow velocity, and the relationship between the IB speed and the IB force. Instead of the Dirac delta function, the Lagrange interpolation polynomial is used to obtain the IB speed from nearby fluid velocity. Typical cases, including the flow around a circular cylinder, shearing flow near a non-slip wall, and circular Couette flow between two inversely rotating cylinders, are simulated to verify and validate the method. It is shown that the present method guarantees the non-slip boundary condition and maintain the overall first-order spatial convergence rate of the conventional immersed boundary method (IBM). The accuracy improvement is obvious for both stationary and moving solid boundaries in both viscous flows and strong shearing flows. To demonstrate application possibility, a mechanical heart valve flow is also simulated, and better agreements with experimental data are achieved compared to those by commercial software.
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    A deformable plate interacting with a non-Newtonian fluid in three dimensions
    (AIP, 2017-08) Zhu, Luoding; Yu, Xijun; Liu, Nansheng; Cheng, Yongguang; Lu, Xiyun; Mathematical Sciences, School of Science
    We consider a deformable plate interacting with a non-Newtonian fluid flow in three dimensions as a simple model problem for fluid-structure-interaction phenomena in life sciences (e.g., red blood cell interacting with blood flow). A power-law function is used for the constitutive equation of the non-Newtonian fluid. The lattice Boltzmann equation (the D3Q19 model) is used for modeling the fluid flow. The immersed boundary (IB) method is used for modeling the flexible plate and handling the fluid-plate interaction. The plate drag and its scaling are studied; the influences of three dimensionless parameters (power-law exponent, bending modulus, and generalized Reynolds number) are investigated.
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    An IB Method for Non-Newtonian-Fluid Flexible-Structure Interactions in Three-Dimensions
    (Tech Science Press, 2019) Zhu, Luoding; Mathematical Sciences, School of Science
    Problems involving fluid flexible-structure interactions (FFSI) are ubiquitous in engineering and sciences. Peskin’s immersed boundary (IB) method is the first framework for modeling and simulation of such problems. This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid, Oldroyd-B fluid, and FENE-P fluid. The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations (D3Q19 model). The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model. Numerical results indicate that the new method is first-order accurate and conditionally stable. To show the capability of the new method, it is tested on three FFSI toy problems: a power-law fluid past a flexible sheet fixed at its midline, a flexible sheet being flapped periodically at its midline in an Oldroyd-B fluid, and a flexible sheet being rotated at one edge in a FENE-P fluid.
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    A three-dimensional immersed boundary method for non-Newtonian fluids
    (Elsevier, 2018-05) Zhu, Luoding; Mathematical Sciences, School of Science
    Fluid-structure-interaction (FSI) phenomenon is common in science and engineering. The fluid involved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSI problems is Peskin's immersed boundary (IB) method. However, most of the IB formulations are based on Newtonian fluids. In this letter, we report an extension of the IB framework to FSI involving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach. The new method is tested on two FSI model problems. Numerical experiments show that the method is conditionally stable and convergent with the first order of accuracy.