CONSERVATIVE TWO-PHASE FLOW SIMULATIONS USING PIECEWISE-QUADRATIC INTERFACE RECONSTRUCTIONS

The volume-of-fluid (VOF) and moment-of-fluid (MOF) methods are widely regarded as state-of-the-art techniques for simulating atomization processes, largely because of their unique ability to conserve mass with machine precision. These methods traditionally employ piecewise-linear interface calculations (PLIC) to produce local geometric approximations of the interface that are used to calculate advective fluxes. However, this choice induces two key limitations: First, because the interface is approximated linearly, the transport of volume fractions is at best second-order accurate, while the estimation of curvature---and thus surface tension---is only zeroth-order accurate. Second, planar approximations often cannot adequately represent interfacial structures whose characteristic length-scales (e.g., radius of curvature or thickness) fall below the grid size. As a result, such features are prone to artificial numerical breakup or coalescence. This talk presents recent work on interface reconstruction using piecewise-quadratic surface patches, which aims to overcome both of these limitations. The effectiveness of these higher-order approximations is evaluated through convergence studies and advection test cases. Finally, we discuss extending the method to more general classes of implicit surfaces.