Three-dimensional, fully adaptive simulations of phase-field fluid models

  • Authors:

  • Hector D. Ceniceros;Rudimar L. Nós;Alexandre M. Roma

  • Affiliations:

  • Department of Mathematics, University of California, Santa Barbara, CA 93106, United States;Departamento Acadêmico de Matemática, Universidade Tecnológica Federal do Paraná, CEP 80230-901, Curitiba, PR, Brazil;Departamento de Matemática Aplicada, Universidade de São Paulo, Caixa Postal 66281, CEP 05311-970, São Paulo, SP, Brazil

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We present an efficient numerical methodology for the 3D computation of incompressible multi-phase flows described by conservative phase-field models. We focus here on the case of density matched fluids with different viscosity (Model H). The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow's disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence.