We describe a system that supports real-time interactive visualization of computational fluid dynamics (CFD) simulations. The system allows a user to place and manipulate visualization primitives, such as isolines and streamlines, during an ongoing simulation process. A user can interactively select and designate regions of the computational mesh for refinement as the simulation progresses, perform remeshing, and see the effects of the refinement on the simulation in real time. The system is being used for the study of two open problems in compressible fluid dynamics. We can interactively explore solutions as they are computed, identify flow field regions containing features of interest, and refine the grid in those regions in order to obtain a better result locally. The ability to visualize live data, and to make changes to the computational setup in real time, has helped us to understand the underlying fundamental CFD simulation issues of these problems in shorter times than would otherwise have been possible.