Related papers: Shock profiles for the non-cutoff Boltzmann equati…
The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…
A one-dimensional discrete Boltzmann model for detonation simulation is presented. Instead of numerical solving Navier-Stokes equations, this model obtains the information of flow field through numerical solving specially discretized…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
A new form of the model collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is derived. One-component and many-component systems are considered. The collision operator proposed takes properly into account the…
Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave-steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic equation with hard sphere collisions from underlying dynamics are considered. In particular, a formalism for the description of the evolution of…
We study the traveling wave solutions of a lattice Boltzmann model for the planar streamer fronts that appear in the transport of electrons through a gas in a strong electrical field. To mimic the physical properties of the impact…
The relativistic shock layer problem was numerically analyzed by using two relativistic Boltzmann-kinetic equations. One is Marle model, and the other is Anderson-Witting model. As with Marle model, the temperature of the gain term was…
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…
This paper concerns a kinetic model of the thermostated Boltzmann equation with a linear deformation force described by a constant matrix. The collision kernel under consideration includes both the Maxwell molecule and general hard…
The kinetic theory of rarefied gases and numerical schemes based on the Boltzmann equation have evolved to the cornerstone of non-equilibrium gas dynamics. However, their counterparts in the dense regime remain rather exotic for practical…
We consider a modified Boltzmann equation which contains, together with the collision operator, an additional drift term that is characterized by a matrix A. Furthermore, we consider a Maxwell gas, where the collision kernel has an angular…
A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas particles. More precisely, starting from a finite…
Continuum-based theories, such as Navier-Stokes equations, have been considered inappropriate for flows under nonequilibrium conditions. In part, it is due to the lack of rotational degrees of freedom in the Maxwell-Boltzmann distribution.…
In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov and ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results…
The exact structure of a shock is computed in a multiple-speed discrete-velocity gas, the nine-velocity gas, wherein the multiplicity of speeds ensures nontrivial thermodynamics. Obtained as a solution of the model Boltzmann equations, the…
In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure…