A fast simulation method with arbitrary viscosity law

. A new approach to DSMC collision modelling, called viscosity-DSMC or μ -DSMC, is described in which the time-averaged temperature is used to set the characteristic collision cross-section in each cell such that the Chapman-Enskog viscosity is that given by any desired viscosity law μ = μ(T), including a curve fit to experimental data. For example, 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, a variable hard sphere collision model can reproduce the viscosity given by the more complicated generalized hard collision model, by making the reference cross-section a function of the temperature. This model is used to calculate the structure of a plane 1D shock and the results agree closely with those from standard DSMC using the GHS model. A particularly simple method is to use the Maxwell VHS model, in which all collision pairs are equally likely, to produce any desired viscosity law. The time-averaged cell temperature is available in standard DSMC as part of the procedures which determine the steady state flow and the new methods are as fast as, or faster than standard DSMC. 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. VISCOSITY OF REAL GASES AND THE VHS MODEL