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The numerical simulation of multiphase flows in Light Water (Nuclear) Reactors, LWRs, for normal, accident, and off-normal operation, and for operational optimization must cover a huge disparity of transient time durations, from milliseconds to years. In addition, our recent work has shown that the application of classical Riemann approaches, which pervade modern computational fluid dynamics (CFD), suffer numerical accuracy degradation, especially for compressible liquid flows. In this setting, all-speed or Mach uniform methods are need which can be accurately and efficiently integrated over a very large range of time scales. Thus we need a multi-time-scale integration approach to compliment our previously documented multi-spatial-scale approach to multiphase flow modeling [1]. This report briefly summarizes our efforts in these areas

All-Speed Methods and Long-Duration Time Integration for Incorporation into the 7-Equation Two-Phase Model