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We present a novel time-stepping method, called Operator Splitting withCapillary Relaxation (OSCAR), for efficient Volume-Of-Fluid simulations ofcapillary-dominated two-phase flow. OSCAR uses operator splitting methods toseparate the viscous drag and the surface tension forces. Different time-stepsare used for the viscous drag steps, controlled by the injection velocity, andfor the capillary relaxation steps, controlled by the velocity of capillarywaves. Although OSCAR induces an additional numerical error of order 0 in timeresulting from the splitting, it is well suited for simulations at lowcapillary number. First, the splitting error decreases with the capillarynumber and at low capillary number, the relaxation steps converge beforereaching their last iteration, resulting in a large speed-up (here up to 250x)compared to standard time-stepping methods. The method is implemented inGeoChemFoam, our OpenFOAM-based CFD solver. Convergence, accuracy andefficiency are demonstrated on three benchmark cases: (1) the steady motion ofan air bubble in a straight 2D microchannel, (2) injection of supercritical CO2in a 3D constricted channel leading to a snap-off, and (3) water drainage in a2D oil-wet micromodel representing a porous media.

GeoChemFoam: Operator Splitting based time-stepping for efficient Volume-Of-Fluid simulation of capillary-dominated two-phase flow