The DSMC Method

More than fifty years have now elapsed since the writing of the first paper on the Direct Simulation Monte Carlo, or DSMC, method. The early DSMC procedures were justifiably regarded with some suspicion and, by modem standards, computers were extremely slow and expensive . The early developments were described in the first monograph written by the author. The title was Molecular Gas Dynamics and it was published by Oxford University Press in 1 976. Given the general lack of acceptance of the DSMC method at that time, the DSMC method was presented in a somewhat tentative manner and appeared only in the later chapters. By the time that the second monograph Molecular Gas Dynamics and the Direct Simulation of Gas Flows appeared in 1 994, the DSMC procedures were sounder and more comprehensive, computers were incomparably faster and, most importantly, the method had become widely accepted. At the same time, the description of the DSMC method was again confmed to the latter half of the book. The background material associated with the words "molecular gas dynamics" has not changed greatly over the past two decades, but almost all the DSMC procedures have been either revised or superseded. The writing of this book has been motivated by the need to document these developments. The background material has been reduced to cover only the results that are necessary to support the description of the DSMC procedures . The 1 994 monograph was concerned with alternative methods and the derivation of the background equations . This affected the order of presentation of the key results that are required for DSMC . This book is not concerned with the derivation of standard equations and the priority is to present them in a form that makes them easily accessible to the user. While this has simplified the task of writing the book, the recent proliferation of DSMC papers that present alternative procedures makes it difficult to assess them all in order to determine the optimum set of procedures. This book is largely based on the procedures that are currently employed by the author, but they are under constant review and will be changed when alternative procedures are found to be preferable. The DSMC results that are presented in this book have been made either with the open source computer code DSMC that forms part of the book or with the DS2V program that is now being made available as source code . It is intended that the scope of the DSMC program will be extended in future versions of the book to the extent that it will eventually become an easily applied universal parallel code with capabilities that go beyond those of the widely used DS2V/3V codes that have, for some years, been freely downloadable as executables from www.gab.com.au. The extension of DSMC to two and three dimensional flows, together with programs for data file production and graphical post-processing will be added in Versions 2 and 3 . It is intended that Version 4 will address parallel processing. Direct Simulation Monte Carlo is a well-established method for the computer simulation of a gas flow at the molecular level. While there is a limit to the size of the flow-field with respect to the molecular mean free path, personal computers now allow solutions well into the continuum flow regime. The method can be applied to basic problems in gas dynamics and practical applications range from microelectromechanics systems (MEMS) to astrophysical flows. DSMC calculations have assisted in the design of vacuum systems, including those for semiconductor manufacture, and of many space vehicles and missions. The method was introduced by the author fifty years ago and it has been the subject of two monographs that have been published by Oxford University Press. It is now twenty years since the second of these was written and, since that time, most DSMC procedures have been superseded or significantly modified. In addition, visual interactive DSMC application programs have been developed that have proved to be readily applicable by non-specialists to a wide variety of practical problems. The computational variables are set automatically within the code and the programs report whether or not the criteria for a good calculation have been met. This book is concerned with the theory behind the current DSMC molecular models and procedures, with their integration into general purpose programs, and with the validation and demonstration of these programs. The DSMC and associated programs, including all source codes, can be freely downloaded through links that are provided in the book. The main accompanying program is simply called the "DSMC program" and, in future versions of the book, it will be applicable to homogeneous (or zero-dimensional) flows through to three-dimensional flow. All DSMC simulations are time-accurate unsteady calculations, but the flow may become steady at large times. The current version of the DSMC code is applicable only to zero and one-dimensional flows and the older DS2V code is employed for the two-dimensional validation and demonstration cases. It is because of this temporary use of the older and well-proven program that the DS2V source code is made freely available for the first time. Most of the homogeneous flow cases are validation studies, but include internal mode relaxation studies and spontaneous and forced ignition leading to combustion in an oxygen-hydrogen mixture. The one-dimensional cases include the structure of a re-entry shock wave that takes into account electronic excitation as well as dissociation, recombination and exchange reactions. They also include a spherically imploding shock wave and a spherical blast wave. The two-dimensional and axially-symmetric demonstration cases range from a typical MEMS flow to aspects of the flow around rotating planets. Intermediate cases include the formation and structure of a combustion wave, a vacuum pump driven by thermal creep, a typical vacuum processing chamber, and the flow around a typical re-entry vehicle