Application of Taylor series expansion and Least-squares-based lattice Boltzmann method to simulate turbulent flows

Lattice Boltzmann method (LBM) has become an alternative method of computing a variety of fluid flows, ranging from low Reynolds number laminar flows to highly turbulent flows. For turbulent flows, non-uniform grids are preferred. Taylor series expansion- and least-squares-based LBM (TLLBM) is an effective and convenient way to extend standard LBM to be used on arbitrary meshes. In order to show its ability to solve turbulent flows, we combine it with k–ω and S-A turbulence models. To validate these combinations, the benchmark problems of the turbulent channel flow and the turbulent flow over a backward facing step at Re = 44 000 are simulated. Our results compare well with the analytical solution and the experimental results of Kim et al. [22]. This shows that the combination of TLLBM with turbulence model can solve turbulent flows effectively.

[1]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

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

[3]  Shiyi Chen,et al.  A Lattice Boltzmann Subgrid Model for High Reynolds Number Flows , 1994, comp-gas/9401004.

[4]  Hudong Chen.  VOLUMETRIC FORMULATION OF THE LATTICE BOLTZMANN METHOD FOR FLUID DYNAMICS : BASIC CONCEPT , 1998 .

[5]  Alejandro L. Garcia,et al.  Stabilization of thermal lattice Boltzmann models , 1995 .

[6]  Sauro Succi,et al.  An Integer Lattice Realization of a Lax Scheme for Transport Processes in Multiple Component Fluid Flows , 1999 .

[7]  C. Shu,et al.  Least-squares-based lattice Boltzmann method: a meshless approach for simulation of flows with complex geometry. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  B. Shi,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2002 .

[9]  郑楚光,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2005 .

[10]  C. Teixeira.  INCORPORATING TURBULENCE MODELS INTO THE LATTICE-BOLTZMANN METHOD , 1998 .

[11]  S. Thangam,et al.  Turbulent Separated Flow Past a Backward-Facing Step: A Critical Evaluation of Two-Equation Turbulence Models , 1991 .

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

[13]  M. Strelets.  Detached eddy simulation of massively separated flows , 2001 .

[14]  Xiaoyi He,et al.  Lattice Boltzmann Method on Curvilinear Coordinates System , 1997 .

[15]  Taehun Lee,et al.  An Eulerian description of the streaming process in the lattice Boltzmann equation , 2003 .

[16]  Golub Gene H. Et.Al.  Matrix Computations, 3rd Edition , 2007 .

[17]  Taehun Lee,et al.  A characteristic Galerkin method for discrete Boltzmann equation , 2001 .

[18]  Ying Liao,et al.  Large Eddy simulations of a stirred tank using the lattice Boltzmann method on a nonuniform grid , 2002 .

[19]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

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

[21]  M. Nallasamy,et al.  Turbulence models and their applications to the prediction of internal flows: a review , 1987 .

[22]  S. Succi,et al.  The lattice Boltzmann equation on irregular lattices , 1992 .

[23]  Gene H. Golub,et al.  Matrix computations , 1983 .

[24]  Sauro Succi,et al.  Turbulent channel flow simulations using a coarse-grained extension of the lattice Boltzmann method , 1996, comp-gas/9610001.

[25]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[26]  Sauro Succi,et al.  Multiscale lattice Boltzmann schemes with turbulence modeling , 2001 .

[27]  I. Demirdzic,et al.  A finite volume method for computation of fluid flow in complex geometries , 1982 .

[28]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[29]  James P. Johnston,et al.  Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step , 1980 .

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