Related papers: On Modeling and Solving the Boltzmann Equation
At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This "bistability effect" - in which electron-electron (Coulomb) collisions play an essential role - is analyzed…
We describe some scaling issues that arise when using lattice Boltzmann methods to simulate binary fluid mixtures -- both in the presence and in the absence of colloidal particles. Two types of scaling problem arise: physical and…
In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) [J. Comput. Phys., Vol. 255, 2013, pp 680-698] originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme…
We present different techniques to numerically solve the equations of motion for the widely studied Discrete Nonlinear Schroedinger equation (DNLS). Being a Hamiltonian system, the DNLS requires symplectic routines for an efficient…
We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model…
In this work, we are interested in the spectrum of the diffusively excited granular gases equation, in a space inhomogeneous setting, linearized around an homogeneous equilibrium. We perform a study which generalizes to a non-hilbertian…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…
This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method…
This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard…
We present a new Monte Carlo method for obtaining solutions of the Boltzmann equation for describing phonon transport in micro and nanoscale devices. The proposed method can resolve arbitrarily small signals (e.g. temperature differences)…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
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…
We propose a new deterministic numerical scheme, based on the discontinuous Galerkin method, for solving the Boltzamnn equation for rarefied gases. The new scheme guarantees the conservation of the mass, momentum and energy. We avoid any…
We provide a rigorous derivation of Boltzmann's kinetic equation from the hard sphere system for rarefied gas, which is valid for arbitrarily long times, as long as the solution to the Boltzmann equation exists. This extends Lanford's…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional…
We present a series of three-dimensional discrete Boltzmann (DB) models for compressible flows in and out of equilibrium. The key formulating technique is the construction of discrete equilibrium distribution function through inversely…
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…