Related papers: An ES-BGK model for vibrational polyatomic gases
We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role.…
We present molecular dynamics simulations of mono- or bidisperse inelastic granular gases driven by vibrating walls, in two dimensions (without gravity). Because of the energy injection at the boundaries, a situation often met…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
In this work, closure of the Boltzmann--BGK moment hierarchy is accomplished via projection of the distribution function $f$ onto a space $\mathbb{H}^{N}$ spanned by $N$-order Hermite polynomials. While successive order approximations…
The Boltzmann equation describes the detailed microscopic behaviour of a dilute gas, and represents the basis of the kinetic theory of gases. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a…
We present an approach for GW calculations of quasiparticle energies with quasi-quadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method…
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 hydrodynamic-type equations, derived by two-side distribution function for a stratified gas in gravity field is applied to a problem of ultrasound. The theory is based on Gross-Jackson kinetic equation, which solution is built…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
The physics of vibrational kinetics in nitrogen-containing plasma produced by collisions with electrons is studied on the basis of recently derived cross sections and rate coefficients for the resonant vibrational-excitation by…
This paper derives transport equations for medium rarefied gases from the Bhatnagar-Gross-Krook (BGK) model kinetic equation using a Hermite polynomial approximation for the monoatomic gas distribution function. We apply the Chapman-Enskog…
We consider a kinetic description of a multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In…
In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in…
We study the linearized kinetic equation of relaxation model which was proposed by Bhatnagar, Gross and Krook (also called BGK model) and solve the dispersion relation. Using the solution of the dispersion relation, we analyze the…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used…
The Borgnakke-Larsen model, widely used in rarefied flow predictions, serves as the mainstream energy-exchange kernel for polyatomic gases. However, it lacks integrability and does not guarantee detailed balance, limiting theoretical…
We study the weakly-interacting Bose gas in both two and three dimensions using a variational approach. In particular we construct the thermodynamic potential of the gas to within ladder approximation and find by minimization an accurate…
We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…
It is shown how the well-known formula for the gravitational energy of self-gravitating regular polytropes of finite mass can be obtained in an elementary way by using Gauss's divergence theorem and the Chandrasekhar virial tensor, without…