Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlapping control volumes. Degrees of …

In recent years, stylized forms of the Boltzmann equation, now going by the name of" Lattice
Boltzmann equation"(LBE), have emerged, which relinquish most mathematical complexities …

INTRODUCTION The nature of type Ia supernovae (SNIa)—thermonuclear explosions of
white dwarf (WD) stars—is an open question in astrophysics. There is a general consensus …

In these lectures we present the basic ideas and recent development in the construction,
analysis, and implementation of ENO (Essentially Non-Oscillatory) and WENO (Weighted …

In this paper, we propose a general time-discrete framework to design asymptotic-
preserving schemes for initial value problem of the Boltzmann kinetic and related equations …

This book gives a general presentation of the mathematical and numerical connections
kinetic theory and conservation laws based on several earlier works with PL Lions and E …

We propose a new and canonical way of writing the equations of gas dynamics in
Lagrangian coordinates in two dimensions as a weakly hyperbolic system of conservation …

We introduce a general framework for kinetic BGK models. We assume to be given a system
of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK …

We present here some numerical schemes for general multidimensional systems of
conservation laws based on a class of discrete kinetic approximations, which includes the …