Imbalance-correction grid-refinement method for lattice Boltzmann flow simulations

To enhance the accuracy and applicability of the zonal grid refinement method for the lattice Boltzmann method, a new method which minimizes the interface imbalances of mass and momentum is developed. This method introduces a correction step for the macroscopic flow variables such as the fluid density and velocity to remove their interface discontinuity. To demonstrate and evaluate the presently developed imbalance correction grid refinement method, large eddy simulations of turbulent channel and square cylinder flows are carried out. By changing the grid arrangement in the turbulent channel flows, it is confirmed that the present method reduces the sensitivity to the location of the grid refinement interface and minimizes the unphysically discontinuous profiles satisfactorily. Furthermore, the present method considerably improves mass conservation of the system, which is particularly important for long time periodical flow simulations. It is also confirmed that the present method generally improves the prediction performance of the square cylinder flows.

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

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

[3]  Lin,et al.  Lattice boltzmann method on composite grids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  F. Durst,et al.  Homogeneity of turbulence generated by static-grid structures , 2010, Journal of Fluid Mechanics.

[5]  J. Korvink,et al.  Cascaded digital lattice Boltzmann automata for high Reynolds number flow. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Emmanuel Lévêque,et al.  Direct and large-eddy simulation of turbulent flows on composite multi-resolution grids by the lattice Boltzmann method , 2014, J. Comput. Phys..

[7]  Sharath S. Girimaji,et al.  LES of turbulent square jet flow using an MRT lattice Boltzmann model , 2006 .

[8]  B. Chopard,et al.  Theory and applications of an alternative lattice Boltzmann grid refinement algorithm. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Manuel V. Heitor,et al.  Measurements of turbulent and periodic flows around a square cross-section cylinder , 1988 .

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

[11]  Lyazid Djenidi.  Lattice-Boltzmann simulation of grid-generated turbulence , 2006, Journal of Fluid Mechanics.

[12]  Li-Shi Luo,et al.  Some Progress in Lattice Boltzmann Method. Part I. Nonuniform Mesh Grids , 1996 .

[13]  Yoshiaki Kuwata,et al.  A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows , 2015, Comput. Math. Appl..

[14]  Sanjoy Banerjee,et al.  On the Three-Dimensional Central Moment Lattice Boltzmann Method , 2011, 1202.6081.

[15]  S. Girimaji,et al.  Multi-block Lattice Boltzmann method: Extension to 3D and validation in turbulence , 2006 .

[16]  Peter M. A. Sloot,et al.  Finite-Difference Lattice-BGK methods on nested grids , 2000 .

[17]  W. Shyy,et al.  Improved treatment of the open boundary in the method of Lattice Boltzmann equation , 2005 .

[18]  Y. Kuwata,et al.  Anomaly of the lattice Boltzmann methods in three-dimensional cylindrical flows , 2015, J. Comput. Phys..

[19]  J. Ferziger,et al.  Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows , 1983 .

[20]  Sharath S. Girimaji,et al.  Direct numerical simulations of homogeneous turbulence subject to periodic shear , 2006, Journal of Fluid Mechanics.

[21]  Orestis Malaspinas,et al.  Advances in multi-domain lattice Boltzmann grid refinement , 2012, J. Comput. Phys..

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

[23]  A. Mochida,et al.  On turbulent vortex shedding flow past 2D square cylinder predicted by CFD , 1995 .

[24]  F. Nicoud,et al.  Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor , 1999 .

[25]  M. J. Pattison,et al.  Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method , 2009, 0901.0593.

[26]  Joel H. Ferziger,et al.  Status of Large Eddy Simulation: Results of a Workshop , 1997 .

[27]  Pierre Sagaut,et al.  A study of time correlations in lattice Boltzmann-based large-eddy simulation of isotropic turbulence , 2008 .

[28]  Yassin A. Hassan,et al.  The effect of lattice models within the lattice Boltzmann method in the simulation of wall-bounded turbulent flows , 2013, J. Comput. Phys..

[29]  D. Kandhai,et al.  A generic, mass conservative local grid refinement technique for lattice‐Boltzmann schemes , 2006 .

[30]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  Makoto Nagaoka,et al.  Large eddy simulation analysis of engine steady intake flows using a mixed-time-scale subgrid-scale model , 2010 .

[32]  Jochen Fröhlich,et al.  Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions , 2005, Journal of Fluid Mechanics.

[33]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[34]  F. Durst,et al.  Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow , 2006 .

[35]  Martin Geier,et al.  The cumulant lattice Boltzmann equation in three dimensions: Theory and validation , 2015, Comput. Math. Appl..

[36]  Shmuel Einav,et al.  A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder , 1995, Journal of Fluid Mechanics.

[37]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

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

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

[40]  C. K. Chong,et al.  Rotational invariance in the three-dimensional lattice Boltzmann method is dependent on the choice of lattice , 2011, J. Comput. Phys..