Related papers: Exact Hydrodynamics of the Lattice BGK Equation

Using and comparing kinetic theory and second-order Chapman-Enskog hydrodynamics, we study the non-conformal dynamics of a system undergoing Bjorken expansion. We use the concept of `free-streaming fixed lines' for scaled shear and bulk…

Nonlinear idempotent operator instead of a linear projection is introduced to derive kinetic models for dense fluids. A new lattice Boltzmann model for compressible two-phase flow is derived based on the Enskog--Vlasov kinetic equation as…

The problem of the derivation of hydrodynamics from the Boltzmann equation and related dissipative systems is formulated as the problem of slow invariant manifold in the space of distributions. We review a few instances where such…

We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convection-diffusion type problems: scalar advection-diffusion,…

We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an arbitrary surface from the Boltzmann equation on the surface.

In this work, the first-order constitutive equations for a relativistic charged gas are obtained based on the Chapman-Enskog expansion of near-equilibrium solutions to the Boltzmann equation by implementing the projection method. To this…

Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional…

In [Phys. Rev. 94 (1954), 511-525], P.L. Bhatnagar, E.P. Gross and M. Krook introduced a kinetic equation (the BGK equation), effective in physical situations where the Knudsen number is small compared to the scales where Boltzmann's…

The open problem of derivation of the relativistic Vlasov equation for the systems of charged particles moving with the velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the…

We present a new kinetic model and its lattice Boltzmann realization for the simulation of compressible, non-ideal fluid flows. The method employs first-neighbour lattices and introduces a consistent set of correction terms constructed via…

For the quantum kinetic system modelling the Bose-Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman-Enskog expansion to derive its hydrodynamic approximations, include both Euler and…

We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design…

We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…

We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…

A general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented. We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case, however, without…

We derive the second-order hydrodynamic equation and the microscopic formulae of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation. Our derivation is based on a novel…

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is…

We prove the existence of non-hydrodynamic solutions to the linear density-dependent BGK equation in $d$ dimensions. Specifically, we show the existence of an initial condition for any Knudsen number $\tau$ for which the dissipation rate of…

In this paper, we present a detailed derivation of relativistic first-order spin hydrodynamics using the Chapman-Enskog method to linearize the nonlocal collision term for massive fermions proposed in \cite{Weickgenannt:2021cuo}, which well…

We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…