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    Structure-Preserving Methods for the Navier-Stokes-Cahn-Hilliard System to Model Immiscible Fluids

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    Type
    Dissertation
    Authors
    Sarmiento, Adel cc
    Advisors
    Parsani, Matteo cc
    Calo, Victor M. cc
    Committee members
    Keyes, David E. cc
    Sun, Shuyu cc
    Efendiev, Yalchin R. cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-12-03
    Embargo End Date
    2018-12-03
    Permanent link to this record
    http://hdl.handle.net/10754/626270
    
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    Access Restrictions
    At the time of archiving, the student author of this dissertation opted to temporarily restrict access to it. The full text of this dissertation became available to the public after the expiration of the embargo on 2018-12-03.
    Abstract
    This work presents a novel method to model immiscible incompressible fluids in a stable manner. Here, the immiscible behavior of the flow is described by the incompressible Navier-Stokes-Cahn-Hilliard model, which is based on a diffuse interface method. We introduce buoyancy effects in the model through the Boussinesq approximation in a consistent manner. A structure-preserving discretization is used to guarantee the linear stability of the discrete problem and to satisfy the incompressibility of the discrete solution at every point in space by construction. For the solution of the model, we developed the Portable Extensible Toolkit for Isogeometric Analysis with Multi-Field discretizations (PetIGA-MF), a high-performance framework that supports structure-preserving spaces. PetIGA-MF is built on top of PetIGA and the Portable Extensible Toolkit for Scientific Computation (PETSc), sharing all their user-friendly, performance, and flexibility features. Herein, we describe the implementation of our model in PetIGA-MF and the details of the numerical solution. With several numerical tests, we verify the convergence, scalability, and validity of our approach. We use highly-resolved numerical simulations to analyze the merging and rising of droplets. From these simulations, we detailed the energy exchanges in the system to evaluate quantitatively the quality of our simulations. The good agreement of our results when compared against theoretical descriptions of the merging, and the small errors found in the energy analysis, allow us to validate our approach. Additionally, we present the development of an unconditionally energy-stable generalized-alpha method for the Swift-Hohenberg model that offers control over the numerical dissipation. A pattern formation example demonstrates the energy-stability and convergence of our method.
    Citation
    Sarmiento, A. (2017). Structure-Preserving Methods for the Navier-Stokes-Cahn-Hilliard System to Model Immiscible Fluids. KAUST Research Repository. https://doi.org/10.25781/KAUST-ZK2VT
    DOI
    10.25781/KAUST-ZK2VT
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-ZK2VT
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; Dissertations; Dissertations; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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