▪ Abstract The principles of and procedures for implementing direct simulation Monte Carlo
(DSMC) are described. Guidelines to inherent and external errors common in DSMC …

We review some recent developments in mathematical aspects of relativistic fluids. The goal
is to provide a quick entry point to some research topics of current interest that is accessible …

The previous chapters presented detailed derivations of various sets of transport equations,
and here we take a step back and collect the equations on a few pages. The chapter begins …

We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid
turbulence and estimate the scale at which they become important. As anticipated by …

Occasionally the continuum description of fluid flows is inadequate and it is necessary to
study the dynamics at finer, microscopic, length and time scales. For example, the solutions …

The primary concern of computational fluid dynamics is the development and application of
numerical methods to solve the partial differential equations of hydrodynamics. 1 These …

A detailed analytical and numerical analysis of a recently introduced stochastic model for
fluid dynamics with continuous velocities and efficient multi-particle collisions is presented. It …

This work is mainly concerned with the extension of hydrodynamics beyond the Navier–
Stokes equations, a regime known as Burnett hydrodynamics. The derivation of the Burnett …

We present two-dimensional direct molecular simulation (DMS) results for high-enthalpy
nitrogen flows in thermochemical non-equilibrium around a circular cylinder. The …

I present a brief history, from my own personal perspective, of molecular dynamics (MD)
computer simulations of shock waves without chemical reaction. Beginning with radiation …