Taylor-series expansion and least-squares-based lattice Boltzmann method: Two-dimensional formulation and its applications

2002 ◽  
Vol 65 (3) ◽  
Author(s):  
C. Shu ◽  
X. D. Niu ◽  
Y. T. Chew
Keyword(s):  
Least Squares ◽  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Taylor Series Expansion ◽  
Two Dimensional ◽  
Boltzmann Method

SIMULATION OF NATURAL CONVECTION IN A SQUARE CAVITY BY TAYLOR SERIES EXPANSION- AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD

2002 ◽  
Vol 13 (10) ◽  
pp. 1399-1414 ◽  
Author(s):  
C. SHU ◽  
Y. PENG ◽  
Y. T. CHEW
Keyword(s):  
Natural Convection ◽  
Least Squares ◽  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Taylor Series Expansion ◽  
Uniform Grid ◽  
Square Cavity ◽  
Boltzmann Method

The Taylor series expansion- and least squares-based lattice Boltzmann method (TLLBM) was used in this paper to extend the current thermal model to an arbitrary geometry so that it can be used to solve practical thermo-hydrodynamics in the incompressible limit. The new explicit method is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least squares approach. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Numerical simulations of natural convection in a square cavity on both uniform and nonuniform grids have been carried out. Favorable results were obtained and compared well with the benchmark data. It was found that, to get the same order of accuracy, the number of mesh points used on the nonuniform grid is much less than that used on the uniform grid.

TAYLOR SERIES EXPANSION AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD: THREE-DIMENSIONAL FORMULATION AND ITS APPLICATIONS

2003 ◽  
Vol 14 (07) ◽  
pp. 925-944 ◽  
Author(s):  
C. SHU ◽  
X. D. NIU ◽  
Y. T. CHEW
Keyword(s):  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
Least Square ◽  
Two Dimensional ◽  
Algebraic Form ◽  
Boltzmann Method

The two-dimensional form of the Taylor series expansion- and least square-based lattice Boltzmann method (TLLBM) was recently presented by Shu et al.8 TLLBM is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least square optimization. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. In this paper, TLLBM is extended to the three-dimensional case. The resultant form keeps the same features as the two-dimensional one. The present form is validated by its application to simulate the three-dimensional lid-driven cavity flow at Re=100, 400 and 1000. Very good agreement was achieved between the present results and those of Navier–Stokes solvers.

NUMERICAL SIMULATION OF FLOWS PAST A ROTATIONAL CIRCULAR CYLINDER BY TAYLOR-SERIES-EXPANSION AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD

2005 ◽  
Vol 16 (11) ◽  
pp. 1753-1770 ◽  
Author(s):  
C. SHU ◽  
K. QU ◽  
X. D. NIU ◽  
Y. T. CHEW
Keyword(s):  
Circular Cylinder ◽  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Taylor Series Expansion ◽  
Least Square ◽  
Mesh Structure ◽  
Boltzmann Method

An explicit Taylor series expansion and least square-based lattice Boltzmann method (TLLBM) is used to simulate the two-dimensional unsteady viscous incompressible flows. TLLBM is based on the well-known Taylor series expansion and the least square optimization. It has no limitation on mesh structure and lattice model. Its marching in time is accurate. Therefore, it is very suitable for simulation of time dependent problems. Numerical experiments are performed for simulation of flows past a rotational circular cylinder. Good agreement is achieved between the present results and available data in the literature.

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