A fast simulation method with arbitrary viscosity law

Abstract

A new approach to DSMC collision modelling, called viscosity-DSMC or mu-DSMC, is described. The characteristic collision cross-section (of any standard collision model) is made to vary from cell to cell, based on the time-averaged temperature in each cell. In this way the collision model will display the Chapman-Enskog viscosity given by any desired viscosity law mu = mu(T), including a curve fit to experimental data. For example, we show that a hard sphere collision model, with hard sphere collision probability, used with a different molecular size in each cell, can reproduce a Sutherland viscosity law. Similarly, by making the reference cross-section of a VHS collision model a function of the temperature, we show that the VHS collision model can reproduce the viscosity given by the more complicated generalized hard sphere (GHS) collision model. We calculate the structure of a plane 1D shock using the new approach and show that the results agree closely with those from standard DSMC using the GHS model. A particularly simple, and computationally efficient, method is to use the Maxwell VHS model, in which all collision pairs are equally likely, as the basis of the new method. That is, the characteristic size of the maxwell VHS model is varied from cell to cell, based on the time-averaged cell temperature and the (arbitrary) desired viscosity law mu = mu(T). Since the time-averaged cell temperature is available in standard DSMC as part of the procedures which determine the steady state flow, the new methods are as fast as, or faster than DSMC using the standard VHS model. Unlike more complicated models with realistic viscosities, the new procedures are compatible with the Borgnakke-Larsen energy exchange scheme and the established chemistry models for DSMC. ©2005 American Institute of Physics