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Development of a Multiblock Solver Utilizing the Lattice Boltzmann and Traditional Finite Difference Methods for Fluid Flow Problems Aditya C

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Development of a Multiblock Solver Utilizing the Lattice Boltzmann and Traditional Finite Difference Methods for Fluid Flow Problems Aditya C Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2008 Development of a multiblock solver utilizing the lattice Boltzmann and traditional finite difference methods for fluid flow problems Aditya C. Velivelli Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Velivelli, Aditya C., "Development of a multiblock solver utilizing the lattice Boltzmann and traditional finite difference methods for fluid flow problems" (2008). Retrospective Theses and Dissertations. 15862. https://lib.dr.iastate.edu/rtd/15862 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Development of a multiblock solver utilizing the lattice Boltzmann and traditional finite difference methods for fluid flow problems by Aditya C Velivelli A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Program of Study Committee: Mark Bryden, Major Professor Richard Pletcher Tom I-P. Shih Richard Hindman James Oliver Iowa State University Ames, Iowa 2008 UMI Number: 3296797 Copyright 2008 by Velivelli, Aditya C. All rights reserved. UMI Microform 3296797 Copyright 2008 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 ii TABLE OF CONTENTS ABSTRACT.................................................................................................................. v CHAPTER 1. INTRODUCTION ................................................................................ 1 1.1 Objectives .......................................................................................................... 4 1.2 Dissertation Organization .................................................................................. 4 CHAPTER 2. BACKGROUND .................................................................................. 6 2.1 Grid Generation ................................................................................................. 6 2.1.1 Cartesian Grid ............................................................................................. 7 2.1.2 Structured Body-Fitted Grid ....................................................................... 9 2.1.3 Unstructured Grid ..................................................................................... 10 2.1.4 Semi-Structured or Prismatic Grid............................................................ 11 2.1.5 Hybrid Grid............................................................................................... 12 2.1.6 Grid Change corresponding to Geometry Changes .................................. 14 2.2 Numerical Solution of Fluid Flow Equations.................................................. 16 2.2.1 Finite Difference Method.......................................................................... 16 2.2.2 Finite Volume Method.............................................................................. 16 2.2.3 Finite Element Method ............................................................................. 17 2.2.4 Explicit and Implicit Methods .................................................................. 18 2.3 Fast Models for CFD ....................................................................................... 18 2.3.1 Low-Fidelity Models ................................................................................ 19 2.3.1.1 Reduced-Basis Method ................................................................... 19 2.3.1.2 Bayesian Methods........................................................................... 21 2.3.2 Fast High-Fidelity Models ........................................................................ 22 2.3.2.1 Using First Order PDEs .................................................................. 23 2.3.2.2 Flow Network Model...................................................................... 24 2.3.2.3 Using Classical Analytical Techniques .......................................... 25 2.3.3 Summary of the Fast Computational Methods ......................................... 26 2.3.4 Lattice Boltzmann Method (LBM) ........................................................... 27 2.4 Multiblock and Multi-Solver Methods ............................................................ 28 2.4.1 Summary of the Multiblock and Multi-Solver Methods........................... 36 CHAPTER 3. THE LATTICE BOLTZMANN METHOD AND CACHE OPTIMIZATION........................................................................................................ 38 3.1 Introduction to the LBM .................................................................................. 38 3.1.1 Applying the Lattice Boltzmann Scheme ................................................. 40 3.1.2 Ansatz Method.......................................................................................... 41 3.1.3 Lattice Boltzmann Algorithm ................................................................... 46 3.1.4 Initial and Boundary Conditions............................................................... 47 3.1.5 Stability and Accuracy of LBM................................................................ 48 3.2 Cache Optimization ......................................................................................... 50 3.1.1 Cache Blocking for the LBM.................................................................... 52 3.3 Parallel LBM.................................................................................................... 60 3.3.1 Domain Decomposition for Parallel Processing....................................... 60 3.3.2 Cache Blocking for the Parallel Lattice Boltzmann Algorithm................ 62 iii 3.3.3 Implementation ......................................................................................... 64 3.3.4 Results....................................................................................................... 65 3.3.5 General Conclusions about the Cache Optimization ................................ 75 3.4 Comparison of Lattice Boltzmann and Traditional Methods .......................... 75 3.4.1 Test Problem ............................................................................................. 76 3.4.2 ADI Method .............................................................................................. 77 3.4.3 Parallel ADI Method................................................................................. 80 3.4.4 ADI Algorithm and Cache Optimization.................................................. 83 3.4.5 Results....................................................................................................... 84 3.4.5.1 Accuracy ......................................................................................... 84 3.4.5.2 Parallel Speedup.............................................................................. 85 3.4.5.3 Relative Speedup ............................................................................ 87 3.4.6 Conclusions from the Comparison Study for Unsteady Burger’s Equation .............................................................................................................. 90 3.4.7 Test Case for a Steady Problem ................................................................ 91 3.4.8 Relative Performance of the LBM and the ADI Method.......................... 92 3.4.8.1 Accuracy ......................................................................................... 92 3.4.8.2 Parallel Speedup.............................................................................. 93 3.4.8.3 Relative Speedup ............................................................................ 93 3.4.9 Conclusions............................................................................................... 94 CHAPTER 4 IMPROVING THE PERFORMANCE OF THE LATTICE BOLTZMANN METHOD FOR STEADY FLOW SIMULATION......................... 97 4.1 Improved LBM ................................................................................................ 98 4.1.1 Improved Stability .................................................................................. 100 4.1.2 Cache Optimization and Parallelization.................................................. 101 4.1.3 Results..................................................................................................... 102 4.1.4 Conclusions............................................................................................. 107 4.2 Coupling LBM with the ADI Method for Solving the Two-Dimensional Burger’s Equation. ................................................................................................ 109 4.2.1 Applying the Hybrid Scheme to Burger’s Equation with Multiblock Grid ................................................................................................................... 110 4.2.2 Coupling Procedure................................................................................
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