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Summary: Three-dimensional, fully adaptive simulations
of phase-field fluid models
Hector D. Ceniceros
Department of Mathematics, University of California, Santa Barbara, CA 93106
Rudimar L. N´os
Departamento Acad^emico de Matem´atica, Universidade Tecnol´ogica Federal do
Paran´a, CEP 80230-901, Curitiba-PR, Brasil
Alexandre M. Roma
Departamento de Matem´atica Aplicada, Universidade de S~ao Paulo, Caixa Postal
66281, CEP 05311-970, S~ao Paulo-SP, Brasil
Abstract
We present an efficient numerical methodology for the 3D computation of incom-
pressible 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 investiga-
tion of the key aspects of AMR in a conservative, phase field setting. We validate the
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