Boundary slip from the immersed boundary lattice Boltzmann models.

We report an interesting and important observation of the velocity fields from immersed boundary lattice Boltzmann methods (IB-LBM). The computed velocity profiles can deviate from theoretical predictions greatly even for very simple flow situations, both in the immersed boundary layer and the bulk region. A rigorous analysis of the IB-LBM simulated velocity for a symmetric shear flow is carried out, and the analytical solutions indicate a strong dependence of velocity on the relaxation parameter (kinetic viscosity). Also our simulations demonstrate that simply increasing the immersed boundary layer thickness is not an efficient approach to reduce such velocity discrepancy. We hope this work will bring the awareness of this essential issue to people using IB-LBM for various flow situations.

[1]  Fuzhi Tian,et al.  A bottom-up approach to non-ideal fluids in the lattice Boltzmann method , 2008 .

[2]  Junfeng Zhang,et al.  Contact line and contact angle dynamics in superhydrophobic channels. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[3]  Junfeng Zhang,et al.  On the validity of the Cassie equation via a mean-field free-energy lattice Boltzmann approach. , 2005, Journal of colloid and interface science.

[4]  Shiyi Chen,et al.  Lattice-Boltzmann Simulations of Fluid Flows in MEMS , 1998, comp-gas/9806001.

[5]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[6]  Daniel Y. Kwok,et al.  ELECTROKINETIC SLIP FLOW OF MICROFLUIDICS IN TERMS OF STREAMING POTENTIAL BY A LATTICE BOLTZMANN METHOD: A BOTTOM-UP APPROACH , 2007 .

[7]  Z. Feng,et al.  The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems , 2004 .

[8]  Marek Cieplak,et al.  Christodoulides, Demetrios N. , 2001 .

[9]  Wei Shyy,et al.  Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids , 1997 .

[10]  Y. T. Chew,et al.  Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows , 2006, J. Comput. Phys..

[11]  Daniel Y. Kwok,et al.  A 2D lattice Boltzmann study on electrohydrodynamic drop deformation with the leaky dielectric theory , 2005 .

[12]  Robert Dillon,et al.  Modeling Biofilm Processes Using the Immersed Boundary Method , 1996 .

[13]  A. Popel,et al.  Large deformation of red blood cell ghosts in a simple shear flow. , 1998, Physics of fluids.

[14]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[15]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[16]  A. Yiotis,et al.  A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains , 2007 .

[17]  Baoming Li,et al.  Mean-field free-energy approach to the lattice Boltzmann method for liquid-vapor and solid-fluid interfaces. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Debra Spinks,et al.  Annual Research Briefs , 1997 .

[19]  C. Peskin,et al.  Interaction of two flapping filaments in a flowing soap film , 2003 .

[20]  Ching Shen,et al.  EXAMINATION OF THE LBM IN SIMULATION OF MICROCHANNEL FLOW IN TRANSITIONAL REGIME , 2004 .

[21]  S Succi,et al.  Generalized lattice Boltzmann method with multirange pseudopotential. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[24]  Lattice Boltzmann BGK model for gas flow in a microchannel , 2008 .

[25]  C. Meinhart,et al.  Apparent fluid slip at hydrophobic microchannel walls , 2002 .

[26]  Klaus Mueller,et al.  Melting and flowing in multiphase environment , 2006, Comput. Graph..

[27]  Wei Shyy,et al.  Multigrid computations with the immersed boundary technique for multiphase flows , 2004 .

[28]  L. Luo,et al.  Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model , 1997 .

[29]  Aleksander S Popel,et al.  Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. , 2005, Journal of biomechanical engineering.

[30]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

[31]  X. Shan.  Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Petros Koumoutsakos,et al.  An immersed boundary-lattice-Boltzmann method for the simulation of the flow past an impulsively started cylinder , 2008, J. Comput. Phys..

[33]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[34]  Aleksander S Popel,et al.  An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows , 2007, Physical biology.

[35]  R. Verzicco,et al.  Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations , 2000 .

[36]  Yan Peng,et al.  A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows , 2006 .

[37]  W. Shyy,et al.  Computational modeling of cell adhesion and movement using a continuum-kinetics approach. , 2003, Biophysical journal.

[38]  Junfeng Zhang,et al.  Apparent slip over a solid-liquid interface with a no-slip boundary condition. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Gretar Tryggvason,et al.  An Adaptive, Cartesian, Front-Tracking Method for the Motion, Deformation and Adhesion of Circulating Cells , 1998 .

[40]  A. Fogelson,et al.  A fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles , 1988 .

[41]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[42]  Chang Shu,et al.  Application of lattice Boltzmann method to simulate microchannel flows , 2002 .

[43]  J R Banavar,et al.  Boundary conditions at a fluid-solid interface. , 2001, Physical review letters.