A highly accurate bound-preserving phase field method for incompressible two-phase flows

In this paper, we propose a phase-field-based spectral element method by solving the Navier–Stokes/Cahn–Hilliard equations for incompressible two-phase flows. With use of Newton–Raphson Cahn–Hilliard equation and time-stepping scheme Navier–Stokes equation, construct three constant (time-independent) coefficient matrixes solutions velocity, pressure, phase variable. Moreover, invoke modified bulk free energy density to guarantee boundness solution equation. The above strategies enhanced computation efficiency accurate capture interfacial dynamics. For canonical tests diagonal motion circle Zalesak's disk rotation, lowest relative errors interface profile in contrast published highlight high accuracy proposed approach. our previous work, present approximately produces only one tenth after rotation cycle but saves 27.2% cost. Furthermore, note that mobility parameter adopted appears produce convergent field distribution chemical potential remains divergent, which thereby results diverse coalescence processes two merging droplets example. Therefore, criterion choice is based on these observations, i.e., should ensure convergence potential. Finally, rising bubble presented verify method's versatility under large (1000) viscosity contrasts (100), its advantage over solver manifested 44.9% savings