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Adaptive, Multi-Domain Techniques for Two-Phase Flow Computations

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Adaptive, Multi-Domain Techniques for Two-Phase Flow Computations ADAPTIVE, MULTI-DOMAIN TECHNIQUES FOR TWO-PHASE FLOW COMPUTATIONS By ERAY UZGÖREN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006 Copyright 2006 by ERAY UZGÖREN To my parents ACKNOWLEDGMENTS Among the many individuals for their support, my most sincere acknowledgements go to my advisor, Dr. Wei Shyy, for providing me the opportunity and flexibility to perform this work. His guidance and encouragement provided me the most excellent source of direction throughout this research. I can not thank him enough for being so patient and understanding for years and pushing us to learn more. I would like to thank Dr. Tony Ladd for his guidance and support in the area of parallel computing. I would also like to express my appreciation to Dr. Jacob Chung, Dr. Renwei Mei, and Dr. Bruce Carroll for their helpful comments and for participating in my dissertation committee. I would like to express my gratitude to my family members; my parents, Hürriyet and İbrahim Uzgören; my sisters and their families, Nilay, Ada and Melih Papila; Emine, Yiğit and Bulent Topoglu for their patience, support and love during these years. They are the undisclosed source of the power that I found in myself at hard times. Finally, I would like to thank to Yasemin Merzifonluoğlu for her endless support. iv TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES........................................................................................................... viii LIST OF FIGURES ........................................................................................................... ix ABSTRACT..................................................................................................................... xiv CHAPTER 1 INTRODUCTION ...................................................................................................1 1.1 Multiphase Flows.........................................................................................1 1.2 Objective and Contributions ........................................................................3 1.3 Outline of the Dissertation...........................................................................6 2 MATERIALS AND METHODS.............................................................................8 2.1 Interface Location ........................................................................................8 2.2 Interfacial Dynamics..................................................................................12 2.3 Computational Efficiency ..........................................................................15 2.3.1 Adaptive Grid Computation...........................................................16 2.3.2 Improvements on Iterative Solvers ................................................18 2.3.3 Parallel Computing ........................................................................19 2.4 Summary....................................................................................................21 3 LITERATURE REVIEW ......................................................................................23 3.1 Domain Decomposition Methods ..............................................................25 3.1.1 Schur Complement Methods..........................................................27 3.1.2 Schwarz Methods...........................................................................30 3.1.3 Applications of Continuous Interface Methods .............................35 3.2 Partitioning.................................................................................................38 3.2.1 Partitioning Techniques .................................................................39 3.2.1.1 Multilevel schemes ............................................................40 3.2.1.2 Space filling curves............................................................41 3.2.2. Quality Considerations...................................................................42 3.2.2.1 Load balancing...................................................................42 3.2.2.2 Communication overhead ..................................................43 v 3.2.2.3 Convergence ......................................................................43 3.2.2.4 Computational time............................................................44 3.3 Summary....................................................................................................44 4 MULTIDIMENSIONAL IMMERSED BOUNDARY COMPUTATION ...........46 4.1 Immersed Boundary Method .....................................................................46 4.1.1 Interface Tracking..........................................................................48 4.1.2 Conservative Reconstruction .........................................................49 4.1.3 Interface Construction for Topology Changes...............................50 4.1.4 Modeling Complex Solid Boundaries............................................52 4.1.5 Interactions between Interface and Computational Domain Boundary........................................................................................55 4.1.6 Connection between Eulerian and Lagrangian variables...............56 4.2 Adaptive Cartesian Grid Based Flow Computations.................................64 4.2.1 Grid Adaptation and Data Structure ..............................................65 4.2.2 Staggered Grid Arrangement .........................................................66 4.2.3 Discretization of Governing Equations..........................................68 4.2.4 Axisymmetric Computations .........................................................73 4.3 Summary....................................................................................................74 5 ADAPTIVE COMPUTATIONS IN MULTIPLE DOMAINS..............................77 5.1 Partitioning Algorithm...............................................................................77 5.1.1 Space Filling Curve Generation.....................................................79 5.1.2 Cell Ordering .................................................................................81 5.1.3 Mapping Partitions.........................................................................82 5.1.4 Overlap Region ..............................................................................83 5.1.4.1 Ghost cells..........................................................................84 5.1.4.2 Ghost faces.........................................................................86 5.1.5 Communication Routines...............................................................87 5.1.6 Grid Adaptation .............................................................................89 5.2 Domain Decomposition for Advection-Diffusion Equation......................90 5.3 Domain Decomposition for Pressure Poisson Equation ............................92 5.3.1 Global Treatment ...........................................................................94 5.3.2 Additive Schwarz Technique.........................................................96 5.3.3 Multigrid Solver.............................................................................98 5.3.3.1 Coarse grid generation .......................................................99 5.3.3.2 Matrix assembly...............................................................101 5.3.3.3 Restriction........................................................................102 5.3.3.4 Prolongation.....................................................................103 5.3.3.5 Scheduling........................................................................103 5.4 Summary..................................................................................................105 vi 6 RESULTS AND DISCUSSION..........................................................................107 6.1 Flow over a Cylinder ...............................................................................108 6.2 Liquid-Plug Flow.....................................................................................112 6.2.1 Steady State Solution ...................................................................115 6.2.2 Time Dependent Plug Propagation ..............................................121 6.2.3 Liquid Plug Flow in Branching Channels....................................122 6.3 Multi-Domain Solution Techniques ........................................................126 6.3.1 Partitioning...................................................................................127 6.3.2 Pressure Poisson Equation in a Single Domain ...........................130 6.3.3 Pressure Poisson Equation in Multiple domains..........................137 6.4 Summary..................................................................................................142 7 SUMMARY AND FUTURE WORK .................................................................145 7.1 Summary..................................................................................................145 7.2 Future Work.............................................................................................146 LIST OF REFERENCES.................................................................................................148 BIOGRAPHICAL SKETCH ...........................................................................................158
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