The unstructured lattice Boltzmann method for non-Newtonian flows

Non-Newtonian models with shear-thinning viscosity are commonly used to solve a variety of complex flow problems. A new finite-volume discretization based upon an unstructured grid is used to integrate the differential form of the lattice Boltzmann equation with a shear-dependent viscosity, using a cell-vertex finite-volume technique. The unknown fields are placed at the nodes of the mesh and evolve on the basis of the fluxes crossing the surfaces of the corresponding control volumes. Numerical results show a satisfactory accuracy also in the case of relatively complex geometries and demonstrate the ability of the method to predict the main features of non-Newtonian flows in straight and stenosed channels.

[1]  S. Orszag,et al.  Extended Boltzmann Kinetic Equation for Turbulent Flows , 2003, Science.

[2]  Abdel Monim Artoli,et al.  Mesoscopic Simulations of Unsteady Shear-Thinning Flows , 2006, International Conference on Computational Science.

[3]  Sauro Succi,et al.  Multiscale Coupling of Molecular Dynamics and Hydrodynamics: Application to DNA Translocation through a Nanopore , 2006, Multiscale Model. Simul..

[4]  J. Boyd,et al.  Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method , 2007 .

[5]  Peter M. A. Sloot,et al.  Unsteady flow in a 2D elastic tube with the LBGK method , 2004, Future Gener. Comput. Syst..

[6]  B. Chopard,et al.  Lattice Boltzmann Simulations of Blood Flow: Non-Newtonian Rheology and Clotting Processes , 2005 .

[7]  K. W. Lee,et al.  Modelling of flow and wall behaviour in a mildly stenosed tube. , 2002, Medical engineering & physics.

[8]  Guy Courbebaisse,et al.  Simulation of generalized Newtonian fluids with the lattice Boltzmann method , 2007 .

[9]  Sauro Succi,et al.  Recent advances of Lattice Boltzmann techniques on unstructured grids , 2005 .

[10]  S. Succi,et al.  Lattice Boltzmann method on unstructured grids: further developments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  G Pontrelli,et al.  Blood flow through an axisymmetric stenosis , 2001, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[12]  J. Buick,et al.  The Lattice Boltzmann equation for modelling arterial flows: review and application , 2003 .

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

[14]  O. Filippova,et al.  Grid Refinement for Lattice-BGK Models , 1998 .

[15]  Hun Jung,et al.  Asymmetric flows of non-Newtonian fluids in symmetric stenosed artery , 2004 .

[16]  So-Hsiang Chou,et al.  Lattice Boltzmann method on irregular meshes , 1998 .

[17]  Sauro Succi,et al.  A Generalised Lattice Boltzmann Equation on Unstructured Grids , 2007 .

[18]  Rafik Ouared,et al.  A lattice Boltzmann simulation of clotting in stented aneursysms and comparison with velocity or shear rate reductions , 2006, Math. Comput. Simul..

[19]  Joel Koplik,et al.  Lattice Boltzmann method for non-Newtonian (power-law) fluids. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Shi Jin,et al.  Physical symmetry and lattice symmetry in the lattice Boltzmann method , 1997 .

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