Taylor series expansion- and least square-based Lattice Boltzmann method: an efficient approach for simulation of incompressible viscous flows

2005 ◽  
Vol 5 (1/2) ◽  
pp. 27 ◽  
Author(s):  
C. Shu ◽  
X.D. Niu ◽  
Y. Peng ◽  
Y.T. Chew
Keyword(s):  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Taylor Series Expansion ◽  
Viscous Flows ◽  
Least Square ◽  
Efficient Approach ◽  
Incompressible Viscous Flows ◽  
Boltzmann Method

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.

SIMULATION OF UNSTEADY INCOMPRESSIBLE FLOWS BY USING TAYLOR SERIES EXPANSION- AND LEAST SQUARE-BASED LATTICE BOLTZMANN METHOD

2002 ◽  
Vol 13 (06) ◽  
pp. 719-738 ◽  
Author(s):  
Y. T. CHEW ◽  
C. SHU ◽  
X. D. NIU
Keyword(s):  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Taylor Series Expansion ◽  
Least Square ◽  
New Method ◽  
Time Accuracy ◽  
Boltzmann Method

In this work, an explicit Taylor series expansion- and least square-based lattice Boltzmann method (LBM) is used to simulate two-dimensional unsteady incompressible viscous flows. The new method is based on the standard LBM with introduction of the Taylor series expansion and the least squares approach. The final equation is an explicit form and essentially has no limitation on mesh structure and lattice model. Since the Taylor series expansion is only applied in the spatial direction, the time accuracy of the new method is kept the same as the standard LBM, which seems to benefit for unsteady flow simulation. To validate the new method, two test problems, that is, the vortex shedding behind a circular cylinder at low Reynolds numbers and the oscillating flow in a lid driven cavity, were considered in this work. Numerical results obtained by the new method agree very well with available data in the literature.

SIMULATION OF THERMAL FLOWS BY TAYLOR SERIES EXPANSION- AND LEAST SQUARE-BASED LATTICE BOLTZMANN METHOD COUPLING WITH MACROSCOPIC THERMAL EQUATION

2003 ◽  
Vol 17 (01n02) ◽  
pp. 161-164
Author(s):  
X. D. NIU ◽  
C. SHU ◽  
Y. T. CHEW
Keyword(s):  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Taylor Series Expansion ◽  
Least Square ◽  
Thermal Source ◽  
Thermal Equation ◽  
Boltzmann Method ◽  
Thermal Flows

In this paper we use the Taylor series expansion- and least square-based lattice Boltzmann method to solve thermal flows. By introducing the "thermal source" into the isothermal lattice Boltzmann equation, and coupling with an explicit evaluation of temperature from the macroscopic thermal equation, the macroscopic property of the thermal flows can be obtained. To show the effectiveness of the method presented, the nature convection in the annulus between concentric horizontal circular and square cylinders was simulated and good results were obtained.

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.

Sign in / Sign up

Export Citation Format

Share Document