  The speed of sound in two-phase pipe flow systems is often several orders of
magnitude greater than the travelling speed of hydraulic information (volume
fractions.) Dynamically simulating such flows requires resolution of acoustic
and hydraulic waves existing at vastly different spatial and temporal scales.
If simulated on the same numerical grid, the need for accuracy in hydraulic
waves will necessitate an exaggerated resolution of acoustic waves. Likewise,
time steps restricted by the speed of sound are small compared to the time
scales active in hydraulic waves. This constitutes a waste of computational
potential. The method proposed herein decouples the hydraulic and acoustic
scales, greatly improving computational efficiency.
  The proposed dual grid method solves a four-equation compressible two-fluid
model on a principal grid which robustly accounts for the pressure evolution
and conserves mass and momentum. An incompressible two-equation model is at the
same time solved on a finer grid, resolving the details of the hydraulic
evolution. Information from both model formulations is coupled through the
terms of the governing transport equations, providing consistency between the
grids. Accurate and finely resolved schemes can then be employed for the
incompressible two-fluid model without suffering from the time and stability
restrictions otherwise enforced by acoustic waves. At the same time, the Hybrid
Central-Upwind flux splitting scheme of Evje and Fl{\aa}tten (2005a) allows for
an explicit and numerically robust treatment of the acoustic waves without
losing hydraulic accuracy.
  The dual grid method is tested against four dissimilar problems. In all
problems, the proposed scheme provided significant increases in computational
efficiency and accuracy as compared with a single grid arrangement.
