An efficient phase-field method for turbulent multiphase flows

• Published in: Journal of computational physics 2021-12, Vol.446, p.110659, Article 110659
• Main Authors: Liu, Hao-Ran, Ng, Chong Shen, Chong, Kai Leong, Lohse, Detlef, Verzicco, Roberto
• Format: Article
• Language: English
• Subjects: Algorithms; Biharmonic term; Coalescing; Computational physics; Computer simulation; Computing costs; Density ratio; Direct numerical simulation; Finite element method; Fluid dynamics; Fluid flow; Grid refinement (mathematics); High performance computation; Mathematical analysis; Multiphase flow; Navier-Stokes equations; Phase-field method; Rayleigh-Benard convection; Shear flow; Single-phase flow; Solvers; Three dimensional flow; Turbulence
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110659

•A phase-field method for 3D direct numerical simulation of turbulent multiphase flows.•A novel scheme for solving the biharmonic term in the Cahn-Hilliard equation.•The method is highly efficient by combining the proposed scheme and FFTs solver.•Topological change of interface, and large density/viscosity ratio are considered.•Results are verified against theoretical, experimental and other numerical data. With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation. This novel scheme can significantly reduce the computational cost while retaining the same accuracy as the original procedure. Our phase-field method is built on top of a direct numerical simulation solver, named AFiD (www.afid.eu) and open-sourced by our research group. It relies on a pencil distributed parallel strategy and a FFT-based Poisson solver. To deal with large density ratios between the two phases, a pressure split method [1] has been applied to the Poisson solver. To further reduce computational costs, we implement a multiple-resolution algorithm which decouples the discretizations for the Navier-Stokes equations and the scalar equation: while a stretched wall-resolving grid is used for the Navier-Stokes equations, for the Cahn-Hilliard equation we use a fine uniform mesh. The present method shows excellent computational performance for large-scale computation: on meshes up to 8 billion nodes and 3072 CPU cores, a multiphase flow needs only slightly less than 1.5 times the CPU time of the single-phase flow solver on the same grid. The present method is validated by comparing the results to previous studies for the cases of drop deformation in shear flow, including the convergence test with mesh refinement, and breakup of a rising buoyant bubble with density ratio up to 1000. Finally, we simulate the breakup of a big drop and the coalescence of O(103) drops in turbulent Rayleigh-Bénard convection at a Rayleigh number of 108, observing good agreement with theoretical results.