The expansion of a supercritical fluid solution through a nozzle is th
e key to one approach for producing microscale particles. It is based
on the hyper-compressibility and the change of the solution capacity o
f the fluid from supercritical fluid conditions (high pressure) in exp
ansion to a lower pressure environment. Simulation of the flow needs a
good approximation of the Riemann problem to this type of fluid, and
an accurate representation of the supercritical state by a suitable Eq
uation of State (EOS), the integration of the equations of the motion
is performed with the implicit TVD scheme of Harten and Yee and solved
with the Alternating Direction (ADI) method. Comparison with several
test problems is given. It shows the reliability of the scheme for cap
turing shock waves and rarefaction waves, for representing the gradien
ts of different variables in the nozzle and the jet, compression and e
xpansion phenomena in the jet, and behaviour of the flow near the crit
ical region.