Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit schem...

A gas of inelastic rough spheres admits a spatially homogeneous base state which turns into a hydrodynamic state after a finite relaxation time. We show that this relaxation time is hardly dependent on the degree of inelasticity but increases dramatically with decreasing roughness. An accurate description of translational-rotational velocity correlations at all times is also provided. At a give...

We provide a complete picture to the self-gravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite volume limit in the grand canonical (GCE), canonical (CE) and microcanonical (MCE) ensembles when (N,V ) → ∞, keeping N/V 1/3 fixed. We compute the equation of stat...

We consider the large time behavior in two types of equations, posed on whole space $\mathbb{R}^d$ : Schrödinger equation with a logarithmic nonlinearity one hand; compressible, isothermal, Euler, Korteweg and quantum Navier–Stokes equations other hand. explain some connections between families show how these may help having an insight all cases. insist specific aspects only, refer to cited art...

We study the Cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics, in which the pressure and the density are related by the γ-law equation p(ρ) ∼ ρ with γ = 1. Our results complete those obtained earlier for γ > 1. We prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method. The proof relies on c...

Abstract. In this work we show existence of global weak solutions for a two-phase gas-liquid model where the gas phase is represented by a general isothermal pressure law whereas the liquid is assumed to be incompressible. To make the model relevant for pipe and well-flow applications we have included external forces in the momentum equation representing respectively wall friction forces and gr...