Abstract :
Recent advances in numerical methods and computer systems make it possible to tackle complicated, more realistic ambient and transient solar wind flows. An overview of the ongoing work performed at the NOAA Space Environment Center is presented with examples illustrating: (a) global.3-D interaction of a CME propagating in structured background solar wind, (b) incorporation of a more realistic ambient solar wind, (c) merging of coronal and heliospheric models to track CMEs, and (d) near-Earth solar wind simulations. The aim is to highlight the complexities confronting numerical modelers in meeting challenges imposed by space weather research and forecasting.