New needs and opportunities drive the development of novel computational methods for the design and safety analysis of light water reactors (LWRs). Some new methods are likely to be three dimensional. Coupling is expected between system codes, computational fluid dynamics (CFD) modules, and cascades of computations at scales ranging from the macro- or system scale to the micro- or turbulence scales, with the various levels continuously exchanging information back and forth. The ISP-42/PANDA and the international SETH project provide opportunities for testing applications of single-phase CFD methods to LWR safety problems. Although industrial single-phase CFD applications are commonplace, computational multifluid dynamics is still under development. However, first applications are appearing; the state of the art and its potential uses are discussed. The case study of condensation of steam/air mixtures injected from a downward-facing vent into a pool of water is a perfect illustration of a simulation cascade: At the top of the hierarchy of scales, system behavior can be modeled with a system code; at the central level, the volume-of-fluid method can be applied to predict large-scale bubbling behavior; at the bottom of the cascade, direct-contact condensation can be treated with direct numerical simulation, in which turbulent flow (in both the gas and the liquid), interfacial dynamics, and heat/mass transfer are directly simulated without resorting to models.