No abstract

No abstract

A novel discretization approach for the Bhatnager-Gross-Krook (BGK) kinetic equation is proposed. A hierarchy of LB models starting from D1Q3 model with increasing number of velocities converging to BGK model is derived. The method inherits properties of the Lattice Boltzmann (LB) method like linear streaming step, conservation of moments. Similar to the finite-difference methods for the BGK model the presented approach describes high-order moments of the distribution function with controllable error. The Sod shock tube problem, the Poiseuille flow between parallel plates and the plane Couette flow are considered for wide range of Knudsen numbers. Good stability and significant increase in precision over the conventional LB models are observed.

In the last few decades many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological, and historical processes. In the present paper we suggest a model of the Nazi Germany invasion of Poland, France, and the USSR based on kinetic theory. We simulate this process with the Cauchy boundary problem for two-element kinetic equations. The solution of the problem is given in the form of a traveling wave. The propagation velocity of a front line depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the front-line velocities agree with the historical data.

No abstract

A novel hybrid computational method based on the discrete-velocity (DV) approximation including the lattice-Boltzmann (LB) technique is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows and LB schemes are employed in continuum flow zones. The schemes are written under the finite-volume (FV) formulation to achieve flexibility of local mesh refinement. The expansion to the Hermite polynomials is used for the coupling of DV and LB solutions. Special attention is paid to the recent high-order and regularized LB models. The linear Couette and Poiseuille flows are analyzed as numerical examples, where a good correspondence with the benchmark solutions is obtained.

No abstract

No abstract