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 …

Monte Carlo is one of the most versatile and widely used numerical methods. Its
convergence rate, O (N− 1/2), is independent of dimension, which shows Monte Carlo to be …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

We consider new implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of
conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability …

Many kinetic models of the Boltzmann equation have a diffusive scaling that leads to the
Navier--Stokes type parabolic equations as the small scaling parameter approaches zero. In …

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

We present new numerical models for computing transitional or rarefied gas flows as
described by the Boltzmann-BGK and BGK-ES equations. We first propose a new discrete …

Computational fluid dynamics (CFD) studies the flow motion in a discretized space. Its basic
scale resolved is the mesh size and time step. The CFD algorithm can be constructed …

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 …

In this article, we propose a new class of finite volume schemes of arbitrary accuracy in
space and time for systems of hyperbolic balance laws with stiff source terms. The new class …