An efficient phase-field method for turbulent multiphase flows

With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose new discretization scheme for biharmonic term (the 4th-order derivative term) Cahn-Hilliard equation. This novel can significantly reduce computational cost while retaining same accuracy as original procedure. Our method is built on top direct numerical simulation solver, named AFiD (www.afid.eu) and open-sourced by our research group. It relies pencil distributed parallel strategy FFT-based Poisson solver. To deal large density ratios between two phases, pressure split [1] has been applied to further costs, implement multiple-resolution algorithm which decouples discretizations Navier-Stokes equations scalar equation: stretched wall-resolving grid used equations, equation use fine uniform mesh. The present shows excellent performance large-scale computation: meshes up 8 billion nodes 3072 CPU cores, flow needs only slightly less than 1.5 times time single-phase solver grid. validated comparing results previous studies cases drop deformation in shear flow, including convergence test mesh refinement, breakup rising buoyant bubble ratio 1000. Finally, simulate big coalescence O(10^3) drops Rayleigh-B\'enard convection at Rayleigh number $10^8$, observing good agreement theoretical results.