We provide a general framework to extend the relative entropy method class of diffusive relaxation systems with discrete velocities. The methodology is detailed in toy case 1D Jin-Xin model under scaling, and provides direct proof convergence limit parabolic equation any interval time, regime where solutions are smooth. Recently, same approach has been successfully used show strong vector-BGK 2...

We compare the lattice Boltzmann method (LBM) and Pseudo-Spectral (PS) method for direct numerical simulation of decaying homogeneous isotropic turbulence. In this study we use the generalized lattice Boltzmann equation (GLBE) with multiple-relaxationtime (MRT) collision model, which overcomes all the apparent defects in the popular lattice BGK equation. We first compare the instantaneous flow ...

The extremely high dimensionality and nonlinearity in the Boltzmann equation bring tremendous difficulties to study of rarefied gas dynamics. This paper addresses a neural network-based surrogate model that provides structure-preserving approximation for fivefold collision integral. notion originates from similarity structure between BGK-type relaxation residual network (ResNet) when particle d...

The often-studied problem known as Kramers’ problem, in the general area of rarefied-gas dynamics, is investigated in terms of a linearized, variable collision frequency model of the Boltzmann equation. A convenient change of variables is used to reduce the general case considered to a canonical form that is well suited for analysis by analytical and/or numerical methods. While the general form...

An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problem of sound-wave propagation in a rarefied gas. The analysis and the numerical work are based on a rigorous form of the linearized Boltzmann equation (for rigid-sphere interactions), and in contrast to many other works formulated (for an infinite m...

Introduction Motivations This thesis is devoted to present some new results in the theory of the semilinear approximations to hydrodynamic equations. More specically, the main purpose of this investigation is to prove the convergence of a class of discrete kinetic approximations , the BGK models, to some hyperbolic and hyperbolic-parabolic systems. These BGK models were introduced by Bathnagar,...