Equilibria for the common two-dimensional, nine-velocity (D2Q9) lattice Boltzmann equation are not uniquely determined by the Navier–Stokes equations. An otherwise undetermined function must be chosen to suppress grid-scale instabilities. By contrast, the Navier–Stokes–Fourier equations with heat conduction determine unique equilibria for a one-dimensional, five-velocity (D1Q5) model on an inte...

We conduct an investigation into the dispersive post-shock oscillations in an entropic lattice-Boltzmann method (ELBM), in particular the entropic lattice-Bhatnagar-Gross-Krook (ELBGK) scheme. Simulations on the one-dimensional shock tube show no benefit in terms of regularization from using ELBGK over the standard LBGK. We also conduct an experiment investigating equipping the LBGK method with...

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of e...

The Taylor series expansionand 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 li...

For a one-dimensional benchmark shock tube problem, we implement the lattice Boltzmann method based on the H theorem [I. Karlin, A. Ferrante, and H. C. Ottinger, Europhys. Lett. 47, 182 (1999)]. Results of simulation demonstrate significant improvement of stability, as compared to realizations without explicit entropic estimations.

The lattice Boltzmann method is employed for simulating the binary flow of Oxygen/Nitrogen mixture passing through a highly dense bed of spherical particles. Simulations are performed based on the latest proposed entropic lattice Boltzmann model for multi-component flows, using the D3Q27 lattice stencil. The curved solid boundary of the particles is accurately treated via a linear interpolation...

In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a onedimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on so...

The three-dimensional dynamics of droplets on inclined and vertical walls in a gravity field is simulated. The dependence of a contact angle on a velocity of contact line is obtained for slow regime and smooth surface. The simulations of a rupture of the liquid films on the nonwettable solid substrate due to the thermocapillary effect (Marangoni effect) are also carried out. The lattice Boltzma...

In this paper, we develop an immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows. The lattice Boltzmann method is utilized to solve the incompressible flow field over a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid–membrane interaction with a Lagrangian representation of the capsule membrane. This algorithm was v...

Microflow has become a popular field of interest due to the advent of microelectromechanical systems. In this work, the lattice Boltzmann method, a particle-based approach, is applied to simulate the two-dimensional isothermal pressure driven microchannel flow. Two boundary treatment schemes are incorporated to investigate their impacts to the entire flow field. We pay particular attention to t...