A model of the lattice Boltzmann method for non-Newtonian fluids was constructed. The shear stress of purely viscous but non-elastic non-Newtonian fluid is a function of shear rate only. For the power-law model, only two constant parameters can cover shear-thinning and shear-thickening fluids. Two power-law models are introduced to the finite difference lattice Boltzmann method. One is a model ...

An immersed interface-lattice Boltzmann method (II-LBM) is developed for modelling fluid-structure systems. The key element of this approach the determination jump conditions that are satisfied by distribution functions within framework lattice when forces imposed along a surface in an incompressible fluid. In initial II-LBM, discontinuity related to normal portion interfacial force sharply res...

We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on central-moment (CM) and multi-relaxation-time (MRT) collision models. The simulation induction equation within approach MHD has been usually devised along lines simplest phenomenological description—the single relaxation time (SRT) mo...

The Lattice Boltzmann Method algorithm is simplified by assuming constant numerical viscosity (the relaxation time fixed at $\tau=1$). This leads to the removal of distribution function from computer memory. To test solver Poiseuille and Driven Cavity flows are simulated analyzed. error solution decreases with grid size L as $L^{-2}$. Compared standard algorithm, presented formulation simpler s...

The simplest and most efficient lattice Boltzmann model that is able to recover the Navier-Stokes equations is based on a single-parameter scattering matrix, where the parameter is the first nonzero eigenvalue of the collision matrix. This simple model, based on a single relaxation time, has many shortcomings. Among these is the lack of freedom to extend the model to complex fluids whose stress...

In this paper, we use a lattice Boltzmann model (LBM) for simulation of rarefied gas flows in microchannels at high and moderate Knudsen numbers. The lattice Boltzmann method uses D2Q9 lattice structure and BGK collision operator with single relaxation time. The solid wall boundary conditions used in this paper are based on the idea of bounceback of the nonequilibrium part of particle distribut...

The phonon thermal conductivity of the Lennard-Jones argon face-centered cubic crystal is predicted between temperatures of 20 K and 80 K using the Boltzmann transport equation under the single-mode relaxation time approximation. The temperature and frequency dependencies of the phonon dispersion and phonon relaxation times are obtained from lattice-dynamics calculations based on the results of...