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

chemical engineering science

A Dual Grid Method for the Compressible Two-Fluid Model which Combines  Robust Flux Splitting Methodology with High-Resolution Capturing of  Incompressible Dynamics