Two‐dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first-order and second-order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth-order RungeKutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two-dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side-by-side. Results of these simulations were extensively compared with the previous numerical data. Copyright (C) 2011 John Wiley & Sons, Ltd.

[1]  Ramesh K. Agarwal,et al.  A COMPACT HIGH-ORDER UNSTRUCTURED GRIDS METHOD FOR THE SOLUTION OF EULER EQUATIONS , 1999 .

[2]  Rémi Abgrall,et al.  On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation , 1994 .

[3]  Dhiraj V. Patil,et al.  Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh , 2009, J. Comput. Phys..

[4]  M. Krafczyk,et al.  An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations , 2006 .

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

[6]  A Lamura,et al.  Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. Ferrari,et al.  NUMERICAL SIMULATION OF FLOW INTERFERENCE BETWEEN TWO CIRCULAR CYLINDERS IN TANDEM AND SIDE-BY-SIDE ARRANGEMENTS , 2001 .

[8]  Chang Shu,et al.  SIMULATION OF SHOCK-WAVE PROPAGATION WITH FINITE VOLUME LATTICE BOLTZMANN METHOD , 2007 .

[9]  M. Tsutahara,et al.  Direct Simulation of the Aeolian Tone by the Finite Volume Lattice Boltzmann Method on Unstructured Grid , 2008 .

[10]  Manfred Krafczyk,et al.  Lattice-Boltzmann simulations in reconstructed parametrized porous media , 2006 .

[11]  S. Succi,et al.  Unstructured lattice Boltzmann method in three dimensions , 2005 .

[12]  Sauro Succi,et al.  Simulating the flow around a circular cylinder with a lattice Boltzmann equation , 1989 .

[13]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[14]  D. Tritton,et al.  Physical Fluid Dynamics , 1977 .

[15]  André Bardow,et al.  Multispeed models in off-lattice Boltzmann simulations. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Manfred Krafczyk,et al.  A parallelisation concept for a multi-physics lattice Boltzmann prototype based on hierarchical grids , 2008 .

[17]  Chang Shu,et al.  Numerical simulation of flows around two circular cylinders by mesh‐free least square‐based finite difference methods , 2007 .

[18]  Manfred Krafczyk,et al.  An upwind discretization scheme for the finite volume lattice Boltzmann method , 2006 .

[19]  Seyed Esmail Razavi,et al.  Flux modelling in the finite-volume lattice Boltzmann approach , 2009 .

[20]  C. Liang,et al.  Effect of tube spacing on the vortex shedding characteristics of laminar flow past an inline tube array: a numerical study , 2009 .

[21]  Chaowei Hu,et al.  No . 98-32 Weighted Essentially Non-Oscillatory Schemes on Triangular Meshes , 1998 .

[22]  George Karypis,et al.  Multilevel k-way Partitioning Scheme for Irregular Graphs , 1998, J. Parallel Distributed Comput..

[23]  Guangwu Yan,et al.  A lattice Boltzmann model for the compressible Euler equations with second‐order accuracy , 2009 .

[24]  Pietro Asinari,et al.  Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders , 2009, J. Comput. Phys..

[25]  F. Lien,et al.  Numerical predictions of low Reynolds number flows over two tandem circular cylinders , 2005 .

[26]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[27]  Simulation Of Unsteady Incompressible Flows By Using Taylor Series Expansion- And Least Square-Based Lattice Boltzmann Method , 2002 .

[28]  Jianzhong Lin,et al.  NUMERICAL SIMULATION OF THE FLOWS OVER TWO TANDEM CYLINDERS BY LATTICE BOLTZMANN METHOD , 2005 .

[29]  L. Luo,et al.  A priori derivation of the lattice Boltzmann equation , 1997 .

[30]  Mengya Wang,et al.  Karman vortex street assisted patterning in the growth of silicon nanowires. , 2007, Chemical communications.

[31]  Chunlei Liang,et al.  High-order accurate simulation of low-Mach laminar flow past two side-by-side cylinders using spectral difference method , 2009 .

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

[33]  M. Delanaye,et al.  Quadratic-Reconstruction Finite Volume Scheme for Compressible Flows on Unstructured Adaptive Grids , 1997 .

[34]  So-Hsiang Chou,et al.  FINITE VOLUME SCHEME FOR THE LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES , 1999 .

[35]  André Bardow,et al.  General characteristic-based algorithm for off-lattice Boltzmann simulations , 2006 .

[36]  Victor Sofonea,et al.  Viscosity of finite difference lattice Boltzmann models , 2003 .

[37]  E. LeBoeuf,et al.  Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Chang Shu,et al.  On Implementation of Boundary Conditions in the Application of Finite Volume Lattice Boltzmann Method , 2002 .

[39]  Lian-xia Li,et al.  An improved r-factor algorithm for TVD schemes , 2008 .

[40]  Xiaoyi He,et al.  Lattice Boltzmann method on a curvilinear coordinate system: Vortex shedding behind a circular cylinder , 1997 .

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

[42]  Sanjay Mittal,et al.  Unsteady incompressible flows past two cylinders in tandem and staggered arrangements , 1997 .

[43]  Sauro Succi,et al.  Unstructured lattice Boltzmann equation with memory , 2006, Math. Comput. Simul..

[44]  S. Turek,et al.  Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows , 2006 .

[45]  Chang Shu,et al.  A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder , 2007, J. Comput. Phys..

[46]  Anthony G. Straatman,et al.  An accurate gradient and Hessian reconstruction method for cell‐centered finite volume discretizations on general unstructured grids , 2009 .

[47]  C. Shu,et al.  Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method , 2004 .

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

[49]  R. Benzi,et al.  Lattice Gas Dynamics with Enhanced Collisions , 1989 .

[50]  Sangmo Kang.  Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers , 2003 .

[51]  Kyung-Soo Yang,et al.  Flow-induced forces on two circular cylinders in proximity , 2009 .

[52]  Jiro Mizushima,et al.  Instability and transition of flow past two tandem circular cylinders , 2005 .

[53]  Wei Shyy,et al.  On the Finite Difference-Based Lattice Boltzmann Method in Curvilinear Coordinates , 1998 .

[54]  Haecheon Choi,et al.  Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160 , 1998 .

[55]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .