Motivation and objectives

Next year will be the fortieth anniversary of Direct Simulation Monte Carlo. It is now understood that DSMC, both in its original formulation or in one of its variants, is a particular case of a class of methods for stochastic approximation of solutions of kinetic equations. Since each DSMC ``dialect'' has its own advantages and drawbacks, we propose to organize a workshop to both assess the current state of computational kinetic theory and to look ahead to what the future holds. While DSMC will be the unifying theme, other numerical methods (e.g., molecular dynamics, quadrature methods) will be discussed.

The participants will span the spectrum ranging from those who have used DSMC since its introduction (including Professor Bird himself) to the next generation of young researchers. Despite the diversity, the organizers anticipate significant interactions among the participants since they are the innovators in this community. Since most of the participants are fluent in a variety of numerical methods the organizers expect to stimulate round-table debates on the relative merits and deficiencies of DSMC versus competing algorithms.

This workshop will gather together active scientists, engineers, and mathematicians in the field of computational kinetic theory. By bringing together researchers studying dilute and semi-dense systems of reacting, granular, colloidal, and charged gases, we anticipate triggering a ``gestalt'' experience as the participants realize the similarities in their problems and, hopefully, discover common ground connecting their various disciplines.

Among the topics we expect to address in the workshop are:

Nanoscale flows - DSMC has been used successfully in the simulation of nanoscale flows, however, the computational cost goes as 1/(Mach number)^2 so very low-speed flows, which are of the greatest interest to industry, are prohibitively expensive to simulate. Is there a way to overcome this barrier (e.g., Boyd's IP method) or are other kinetic algorithms more effective for the computation of low-speed, high Knudsen number flows?

Fluctuations and instabilities - DSMC has proved useful in the study of hydrodynamic fluctuations; could it also be used for the simulation of Brownian motors or Feynman ratchet machines? What about the study of instabilities and the effect of fluctuations on those transitions? Are there ways to improve DSMC's efficiency for the simulation of transient flows (e.g., weighted particle schemes) without losing the correct microscopic physics?

Dense gases, liquids, and granular flows - To what extent are DSMC-type methods for dense systems competitive with molecular dynamics or with mesoscale models, such as dissipative particle dynamics (DPD) or lattice Boltzmann?

Multiscale simulation methods - Several types of particle/continuum hybrids have been successfully demonstrated by several of the participants (Boyd, Garcia, Hadjiconstantinou, Klar). What challenges remain before these multiscale methods are practical for solving large-scale problems? Can the lessons learned from DSMC-based hybrids be applied to other types of schemes?

The discussions of the above and related topics will promote a better understanding of the different range of validity, usefulness, or potential for development of various particle-based algorithms

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