相关论文: An Approximate Analytical Solution to Knudsen Laye…

In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…

The classical formalism of the Moment Problem has been combined with a cumulant approach and applied to the extensive many-body problem. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the…

This paper aims to justify the Maxwell-Boltzmann approximation for electrons, preserving the dynamics of ions at the kinetic level. Under sufficient regularity assumption, we provide a precise scaling where the Maxwell-Boltzmann…

This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…

We provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the…

In the current work we construct a multimolecule random process which leads to the Boltzmann equation in the appropriate limit, and which is different from the deterministic real gas dynamics process. We approximate the statistical…

Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…

Various systems of moment equations---consisting of up to (d+3)(d^2+6d+2)/6 moments---in a general dimension d for a dilute granular gas composed of Maxwell molecules are derived from the inelastic Boltzmann equation by employing the Grad…

In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…

Exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at non-vanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of…

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability…

The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the…

The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place…

We propose a multiple relaxation time Boltzmann equation collision model by systematically assigning a separate relaxation time to each of the central moments of the distribution function. The Chapman-Enskog calculation leads to correct…

We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the…

We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given by the wave equation. Coupling conditions for the macroscopic…

We generalize a recent prescription for the relaxation time approximation for the relativistic Boltzmann equation for systems with multiple particle species at finite temperature. This is performed by adding counter-terms to the traditional…

A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…

Thermal wall is a convenient idealization of a rapidly vibrating plate used for vibrofluidization of granular materials. The objective of this work is to incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes…

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…