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 …

Abstract In 1968, Bengt Carlson and Kaye Lathrop published a comprehensive review on
the state of the art in discrete-ordinates (SN) calculations [10]. At that time, SN methodology …

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 …

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 a recent article (Larsen, Morel, and Miller, J. Comput. Phys. 69, 283 (1987)), a theoretical
method is described for assessing the accuracy of transport differencing schemes in highly …

We propose a new numerical scheme for linear transport equations. It is based on a
decomposition of the distribution function into equilibrium and nonequilibrium parts. We also …

Hyperbolic systems often have relaxation terms that give them a partially conservative form
and that lead to a long-time behavior governed by reduced systems that are parabolic in …