In this paper, a simple method is proposed to obtain steady analytical solutions for the lattice Boltzmann method. Based on such analytical results, it is demonstrated how the accuracy of the lattice Boltzmann method can depend on the relative orientation of the lattice and the flow field. It is also demonstrated that the method can be useful to obtain a general class of analytical solutions fo...

The author has recently proposed a macroscopic lattice Boltzmann method (MacLAB) for the Navier–Stokes equations. is formulated first time to retain streaming step by removing collision in two integral steps of standard method. It relies on one fundamental parameter size ?x model. This leads revolutionary and precise minimal “Lattice” method, which directly uses physical variables as boundary c...

In this paper, Lattice Boltzmann Method (LBM) is used to study laminar flow with mixed convection heat transfer inside a two-dimensional inclined lid-driven rectangular cavity with aspect ratio AR = 3. Bottom wall of the cavity is maintained at lower temperature than the top lid, and its vertical walls are assumed insulated. Top lid motion results in fluid motion inside the cavity. Inclination ...

For lattice Boltzmann methods based on entropy functions, we derive a collision integral which enables simple identification of transport coefficients, and which circumvents construction of the equilibrium. Implementation of the two-dimensional hydrodynamics demonstrates considerable increase of stability with respect to conventional lattice Boltzmann schemes.

In this paper, Lattice Boltzmann Method (LBM) is used to study laminar flow with mixed convection heat transfer inside a two-dimensional inclined lid-driven rectangular cavity with aspect ratio AR = 3. Bottom wall of the cavity is maintained at lower temperature than the top lid, and its vertical walls are assumed insulated. Top lid motion results in fluid motion inside the cavity. Inclination ...

We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different sets of lower and higher order are consistently efficiently coupled, allowing us to use the higher-order model only when where needed. This includes regions high Mach or Knudsen numbers. The coupling procedure discrete consists either projection populations onto lower-order lifting B...