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

Handle URI:
http://hdl.handle.net/10754/626270
Title:
Structure-Preserving Methods for the Navier-Stokes-Cahn-Hilliard System to Model Immiscible Fluids
Authors:
Sarmiento, Adel F. ( 0000-0003-0668-2084 )
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.
Advisors:
Parsani, Matteo ( 0000-0001-7300-1280 ) ; Calo, Victor M. ( 0000-0002-1805-4045 )
Committee Member:
Keyes, David E. ( 0000-0002-4052-7224 ) ; Sun, Shuyu ( 0000-0002-3078-864X ) ; Efendiev, Yalchin R. ( 0000-0001-9626-303X )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
3-Dec-2017
Type:
Dissertation
Appears in Collections:
Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorParsani, Matteoen
dc.contributor.advisorCalo, Victor M.en
dc.contributor.authorSarmiento, Adel F.en
dc.date.accessioned2017-12-03T12:23:49Z-
dc.date.available2017-12-03T12:23:49Z-
dc.date.issued2017-12-03-
dc.identifier.urihttp://hdl.handle.net/10754/626270-
dc.description.abstractThis 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.en
dc.language.isoenen
dc.subjectimmiscibleen
dc.subjectincompressibleen
dc.subjectstructure-preservingen
dc.subjectdivergence-conformingen
dc.subjectNavier-Stokes-Cahn-Hilliarden
dc.titleStructure-Preserving Methods for the Navier-Stokes-Cahn-Hilliard System to Model Immiscible Fluidsen
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen
dc.contributor.committeememberKeyes, David E.en
dc.contributor.committeememberSun, Shuyuen
dc.contributor.committeememberEfendiev, Yalchin R.en
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameDoctor of Philosophyen
dc.person.id124246en
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