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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Taylor series expansion- and least-square-based Lattice Boltzmann method (TLLBM) is a flexible Lattice Boltzmann approach capable of simulating incompressible viscous flows with arbitrary geometry. The method is based on the standard Lattice Boltzmann equation (LBE), Taylor series expansion and the least square optimisation. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Successful applications of isothermal and thermal incompressible viscous flows have shown that the TLLBM is an efficient and promising version of LBM. In this paper, we will give the details of TLLBM and present some examples of its application. [ABSTRACT FROM AUTHOR]

The two-dimensional form of the Taylor series expansion- and least square-based lattice Boltzmann method (TLLBM) was recently presented by Shu et al.[sup 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Taylor series expansion- and least squares-based lattice Boltzmann method (TLLBM) is used in this paper to extend the internal energy density distribution function (IEDDF) thermal model to be used on the arbitrary geometry in order to solve practical thermo-hydrodynamics in incompressible limit. The TLLBM essentially has no limitation on the mesh structure and the lattice model. Its use in the thermal model was validated by the numerical simulation of natural convection in a square cavity. Then its application on the curved boundary, natural convection in concentric annuli, was carried out. Favorable results were obtained and compared well with the benchmark data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]