Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field method

We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible of single phase flow is extended to simulate immiscible flows with discontinuous changes in fluid properties such as density and viscosity across the interface. The Navier-Stokes equations conservative field equation interface capturing are first transformed into framework. counter part these smooth obtained by substituting differential forms operators. prove boundedness method order Euler forward predictor-corrector time integration schemes DEC With proper choice two free parameters, remains bounded without requirement any ad hoc mass redistribution. verify against several standard test cases (for capturing) comprising not only flat domains but also curved domains, leveraging advantage that operators independent coordinate system. results show excellent boundedness, conservation convergence. Moreover, we demonstrate ability towards handling large ratios well surface tension simulation various physical phenomena on or surfaces.