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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)

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)

We compare the lattice Boltzmann equation (LBE) and the gas-kinetic scheme (GKS) applied to 2D incompressible laminar flows. Although both methods are derived from the Boltzmann equation thus share a common kinetic origin, numerically they are rather different. The LBE is a finite difference method, while the GKS is a finite-volume one. In addition , the… (More)

In this paper we present a product system and give a representation for cosine functions with the system. Based on the formula, two new algorithms are designed for computing the discrete cosine transform. Both algorithms have a regular recursive structure and good numerical stability and are easy to be implemented on parallel computers. Furthermore, this… (More)

A lattice Boltzmann model is proposed to asses the impact of variable molecular transport effects on the heat and mass transfer in a horizontal shallow cavity due to natural convection. The formulation includes a generalized form of the Soret and Dufour mass and heat diffusion (cross diffusion) vectors derived from non-equilibrium thermodynamics and… (More)

While the lattice Boltzmann method (LBM) has become a powerful numerical approach for solving complex flows, the standard LBM typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions. For inhomogeous and anisotropic flows, it is desirable to have a LBM model that utilizes a rectangular grid. There were two… (More)