Until recently, computer simulation of filling flows in die casting have been focused on the determination of the free surfaces of injected liquid and has had difficulties to relate the flows with the formation of casting porosity. Flow visualization in scaled experiments indicates that the liquid has very complicated surfaces and that, in many cases, the surfaces break up and create a mixture zone with liquid droplets and air. This is especially true in pressure die casting where liquid metal is injected at a speed in order of 100 m/s and at a pressure up to 100 atm. The Reynolds number in the process could be above 105 and the Weber number above 102. Surface tension is far from sufficiently strong to sustain disturbance growth due to various instabilities. It is hard to keep the liquid as a separate continuous phase.
Based on flow visualization experiments, a mathematical model is proposed as an alternative and effective simplification to the traditional tracing methods. Instead of determining the continuous free surfaces, the model tries to predict distributions of mass fraction of the injected liquid by solving a partial differential equation of mass transport together with the Navier-Stokes equations. Appropriate unsteady schemes of a finite difference analysis have been developed and are described in the paper. Results with an uniform straight injection into a die cavity are presented, which have re-created the filling patterns of the flows in experiments.