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We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Several other existing force treatments(More)
In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the(More)
In this paper, a finite-difference-based lattice Boltzmann (LB) algorithm is proposed to simulate electro-osmotic flows (EOF) with the effect of Joule heating. This new algorithm enables a nonuniform mesh to be adapted, which is desirable for handling the extremely thin electrical double layer in EOF. The LB algorithm has been validated by simulating a(More)
In this paper we propose a preconditioned lattice Boltzmann (LB) method for steady incompressible flows. For steady flows, the macroscopic equations derived from this LB model are equivalent to those from the standard LB model, but with an improved eigenvalue system. The proposed model can be viewed as an explicit solver for preconditioned compressible(More)
A lattice Boltzmann model is proposed for solving low Mach number thermal flows with viscous dissipation and compression work in the double-distribution-function framework. A distribution function representing the total energy is defined based on a single velocity distribution function, and its evolution equation is derived from the continuous Boltzmann(More)
Our recent efforts focusing on improving the lattice Boltzmann method (LBM) are introduced, including an incompressible LB model without compressible effect, a flexible thermal LBM with simple structure for Bousinesq fluids, and a robust boundary scheme. We use them to simulate the lid-driven cavity flow at Reynolds numbers 5000–50000, the natural(More)
The standard lattice Boltzmann equation (LBE) is inadequate for simulating gas flows with a large Knudsen number. In this paper we propose a generalized lattice Boltzmann equation with effective relaxation times based on a recently developed generalized Navier-Stokes constitution [Guo, Europhys Lett. 80, 24001 (2007)] for nonequilibrium flows. A kinetic(More)
Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect,(More)
In this paper, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwell-Boltzmann distribution, we obtain a Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit. The continuous thermal BGK model is then discretized over both time and(More)
In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is(More)