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 …

We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

Many real-world problems involve fluids in motion. The goal of this book is to propose a new
approach to numerical analysis of the underlying nonlinear equations in the spirit of the …

We present an Asymptotic-Preserving 'all-speed'scheme for the simulation of compressible
flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based …

This paper presents an asymptotic preserving (AP) all Mach number finite volume shock
capturing method for the numerical solution of compressible Euler equations of gas …

This article deals with the development of a numerical method for the compressible Euler
system valid for all Mach numbers: from extremely low to high regimes. In classical fluid …

We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics
equations. By all regime, we mean that the numerical scheme is able to compute accurate …

In the numerical simulation of fluid dynamic problems there are situations in which acoustic
waves are very fast compared to the average velocity of the fluid and conversely situations in …

Hyperbolic and kinetic equations often possess small spatial and temporal scales that lead
to various asymptotic limits. Numerical approximation of these equations is challenging due …

In this paper we will present and analyze a new class of the IMEX finite volume schemes for
the Euler equations with a gravity source term. We will in particular concentrate on a singular …