kevin thesis draft

A COMPUTATIONAL FRAMEWORK BASED ON AN

EMBEDDED BOUNDARY METHOD FOR HIGHLY NONLINEAR

MULTI-PHASE FLUID-STRUCTURE INTERACTIONS

A DISSERTATION

SUBMITTED TO THE INSTITUTE FOR COMPUTATIONAL

AND MATHEMATICAL ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Kevin Guanyuan Wang

September 2011

Preface

TODO. This thesis tells you all you need to know about life, the universe, and every-

thing.

iv

Acknowledgements

TODO. thanks.

v

Contents

Preface iv

Acknowledgements v

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Underwater implosion . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Unmanned aerial vehicles (UAVs) . . . . . . . . . . . . . . . . 1

1.1.3 Pipeline explosion . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Thesis Accomplishments and Outline . . . . . . . . . . . . . . . . . . 2

1.3.1 Thesis accomplishments . . . . . . . . . . . . . . . . . . . . . 2

1.3.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Mathematical Models 4

2.1 Fluid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.2 Equations of State . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Structure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Constitutive laws . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.3 Fracture criterion . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.4 Cohesive model . . . . . . . . . . . . . . . . . . . . . . . . . . 5

vi

2.3 Fluid-Structure Transmission Conditions . . . . . . . . . . . . . . . . 5

2.4 One-Dimensional Models: Riemann Problems . . . . . . . . . . . . . 5

2.4.1 Single-phase fluid Riemann problems . . . . . . . . . . . . . . 5

2.4.2 Multi-phase fluid Riemann problems . . . . . . . . . . . . . . 6

2.4.3 Fluid-structure Riemann problems . . . . . . . . . . . . . . . 6

3 Computational Framework 7

3.1 Partitioned Procedure for Fluid-Structure Interaction Problems . . . 7

3.2 Finite Volume Based Single and Multi-Phase Compressible Flow Solver 7

3.3 Finite Element Based Structural Solver . . . . . . . . . . . . . . . . . 8

3.4 Numerical Methods for Dynamic Fracture . . . . . . . . . . . . . . . 8

3.5 Embedded/Immersed Boundary Method for Fluid with Moving/Deforming

Boundaries and Fluid-Structure Interactions . . . . . . . . . . . . . . 8

4 Interface Tracking 9

4.1 Tracking An Embedded Fluid-Structure Interface . . . . . . . . . . . 9

4.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.1.2 A projection-based approach . . . . . . . . . . . . . . . . . . . 9

4.1.3 A collision-based approach . . . . . . . . . . . . . . . . . . . . 10

4.1.4 Distributed bounding box hierarchy (scoping) . . . . . . . . . 10

4.1.5 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . 10

4.2 Tracking An Immersible Fluid-Fluid Interface . . . . . . . . . . . . . 11

4.2.1 Level-set equation . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2.2 Implementation details . . . . . . . . . . . . . . . . . . . . . . 11

5 Interface Treatment 12

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.2 Enforcement of the No-Interpenetration Transmission Condition . . . 12

5.2.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.2.2 Numerical accuracy study . . . . . . . . . . . . . . . . . . . . 13

5.3 Enforcement of the Equilibrium Transmission Condition . . . . . . . 13

vii

5.3.1 A numerical algorithm for load computation based on the local

reconstruction of embedded interfaces. . . . . . . . . . . . . . 13

5.3.2 A reconstruction-free algorithm for load computation . . . . . 13

5.3.3 Numerical accuracy study . . . . . . . . . . . . . . . . . . . . 14

6 Applications 15

6.1 Applications in aeronautics . . . . . . . . . . . . . . . . . . . . . . . . 15

6.1.1 Verification for a steady flow around an aircraft wing for HALE

flights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.1.2 Verification for a transient flow past a heaving AGARD wing . 15

6.1.3 Application to the fluid-structure interaction problem with ultra-

thin flapping wings . . . . . . . . . . . . . . . . . . . . . . . . 15

6.2 Applications in underwater implosion and explosion . . . . . . . . . . 16

6.2.1 Validation for the implosive collapse of an air-backed aluminum

cylinder submerged in water (IMP69) . . . . . . . . . . . . . . 16

6.2.2 Application to the explosion-driven fracture propagation of an

air-backed aluminum cylinder submerged in water. . . . . . . 16

6.3 Application in gaseous detonation . . . . . . . . . . . . . . . . . . . . 17

7 Conclusions and Perspectives for Future Work 18

viii

List of Tables

ix

List of Figures

x

Chapter 1

Introduction

1.1 Motivation

1.1.1 Underwater implosion

describe the Navy project.

1.1.2 Unmanned aerial vehicles (UAVs)

flapping wings: what are they? why are they important? relation to the topicof this thesis.

HALE: same as above.

1.1.3 Pipeline explosion

what is it? why is it important? relation to this thesis. (read T-W Chaosthesis)

1.1.4 Summary

summarize the features of these highly nonlinear fluid-structure interactionproblems: (1) strong shock waves; (2) large structural deformation; (3) crack

1

CHAPTER 1. INTRODUCTION 2

propagation; (4) multiple fluid media with large density jump across interface.

the difficulties (including high cost) for performing experiments, which leads tothe call for numerical simulations.

1.2 Objectives

development, verification, and validation of a computational framework for thesimulation of highly nonlinear fluid-structure interaction problems. Describe

the main components and targeted problems/applications.

1.3 Thesis Accomplishments and Outline

1.3.1 Thesis accomplishments

development of an embedded boundary method which includes: (1) interfacetracking techniques for open, closed, and cracking surfaces; (2) a numerical al-

gorithm based on the solution of local fluid-structure Riemann problems for the

enforcement of no-interpenetration transmission condition; (3) two energy con-

serving algorithms for the enforcement of equilibrium transmission conditions.

combination of (1)the fore-mentioned embedded boundary method, (2)a multi-phase flow solver, and (3)an XFEM structure solver into a unified computational

framework.

verification and validation of this computational framework in several appli-cations including underwater implosion, flapping wings, HALE, and pipeline

explosion.

demonstration of its capability of handling multi-phase fluid-structure interac-tions with cracking.

comparison of the embedded boundary method and ALE in terms of capabilityand efficiency.

CHAPTER 1. INTRODUCTION 3

1.3.2 Outline

Chapter 2

Mathematical Models

2.1 Fluid Model

2.1.1 Governing equations

conservation of mass, momentum, and energy. Derive the Navier-Stokes Eqs.

viscosity can be neglected for many applications in this thesis. Reduce to EulerEqs.

to close the system, need an equation of state.

2.1.2 Equations of State

perfect gas: idea, properties, usage.

stiffened gas: idea, properties, usage.

barotropic liquid: idea, properties, usage.

2.2 Structure Model

this section can be relatively short.

4

CHAPTER 2. MATHEMATICAL MODELS 5

2.2.1 Governing equations

a brief description.

include cohesive force at cracks.

2.2.2 Constitutive laws

stress-strain relationship. elastic and elasto-plastic.

cohesive laws.

2.2.3 Fracture criterion

briefly describe the fracture criterion implemented in DYNA3D-XFEM. (pre-sented in Jeong-Hoons thesis)

2.2.4 Cohesive model

2.3 Fluid-Structure Transmission Conditions

no interpenetration (1)for viscous flows; (2)for inviscid flows.

equilibrium (1)for viscous flows; (2)for inviscid flows.

2.4 One-Dimensional Models: Riemann Problems

2.4.1 Single-phase fluid Riemann problems

setup of the Riemann problem.

solution procedure.

importance in FVM.

CHAPTER 2. MATHEMATICAL MODELS 6

2.4.2 Multi-phase fluid Riemann problems

setup.

solution procedure.

2.4.3 Fluid-structure Riemann problems

setup.

solution procedure.

one or two examples with analytical solutions plotted.

Chapter 3

Computational Framework

3.1 Partitioned Procedure for Fluid-Structure In-

teraction Problems

briefly go over different (monolithic and partitioned, strong and weak, etc)coupling approaches.

provide the outline of a typical partitioned procedure.

3.2 Finite Volume Based Single and Multi-Phase

Compressible Flow Solver

semi-discretization of the Euler Equations for a single-phase flow.

treatment of immersible fluid-fluid interfaces: GFM, GFMP, GFMPAR.

tracking the evolution of an immersible fluid-fluid interface: level-set equation.

a brief description of explicit and implicit time-integrators.

7

CHAPTER 3. COMPUTATIONAL FRAMEWORK 8

3.3 Finite Element Based Structural Solver

(this section can be relatively short.)

semi-discretization.

time integrators.

3.4 Numerical Methods for Dynamic Fracture

(this section can be short.)

different methods: element deletion/erosion, interelement crack, remeshing,XFEM.

phantom node formulation.

implementation details in DYNA3D-XFEM.

3.5 Embedded/Immersed Boundary Method for Fluid

with Moving/Deforming Boundaries and Fluid-

Structure Interactions

introduction: basic idea, history, and different approaches.

interface tracking.

interface treatment: (1)for fluid with moving/deforming boundaries; (2)forfluid-structure interactions.

Chapter 4

Interface Tracking

(The 2011 IJNMF paper goes here.)

4.1 Tracking An Embedded Fluid-Structure Inter-

face

4.1.1 Overview

context: 3D, tetrahedral fluid mesh, 2D embedded interface discretized usingtriangles.

input and output of an interface tracker.

briefly go through existing methods.

introduce and compare the two methods to be presented.

4.1.2 A projection-based approach

present the algorithm (step 1, step 2, etc).

discuss the efficiency.

9

CHAPTER 4. INTERFACE TRACKING 10

limitations: (1) cannot handle open surfaces; (2) not accurate if the discreteembedded interface is not well-resolved by the CFD grid.

4.1.3 A collision-based approach

present the algorithm (step 1, step 2, etc).

discuss the efficiency. compare with the projection-based approach.

advantages over the projection-based approach: (1) handles open surfaces; (2)more accurate when the discrete embedded interface is not well-resolved by the

CFD grid.

4.1.4 Distributed bounding box hierarchy (scoping)

context: fluid solved by a parallel solver on a big mesh; structure solved by asequential solver.

the idea and implementation of scoping.

4.1.5 Numerical examples

a rigid AGARD wing: show the intersecting edges obtained from the two meth-ods; show the subdomain scopes.

a cylinder: show the intersecting edges obtained from the two methods.

a flapping wing: show fluidId and intersecting edges obtained from the collision-based approach.

(in these examples, no need to mention the physics.)

CHAPTER 4. INTERFACE TRACKING 11

4.2 Tracking An Immersible Fluid-Fluid Interface

4.2.1 Level-set equation

briefly discuss the solution of the level-set equation and the conservative level-set equation.

4.2.2 Implementation details

mainly discuss the tracking of a fluid-fluid interface which occurs after the crack-ing of a structure.

Chapter 5

Interface Treatment

(The 2010 IJNMF paper goes here.)

5.1 Overview

what is interface treatment (1)for fluid with moving/deforming boundary;(2)for fluid-structure interaction?

briefly summarize existing methods.

context: 3D tetrahedral mesh, finite volume method, fluid-structure interaction.

briefly introduce the methods to be presented.

5.2 Enforcement of the No-Interpenetration Trans-

mission Condition

5.2.1 Algorithm

describe the algorithm. (step 1, step 2, ...)

mention Xianyis work on extending it to 2nd-order.

12

CHAPTER 5. INTERFACE TREATMENT 13

briefly go over implementation details in AERO-F.

5.2.2 Numerical accuracy study

present the piston problem (simulation done in 3D). order = 1.1(inf-norm)/1.4(2-norm)/1.46(1-norm).

5.3 Enforcement of the Equilibrium Transmission

Condition

5.3.1 A numerical algorithm for load computation based on

the local reconstruction of embedded interfaces.

present the algorithm for reconstructing an embedded discrete interface.

present the algorithm for computing the generalized and total flow-induced loadvectors. derive the formulas.

present the conservation and consistency properties.


5.3.2 A reconstruction-free algorithm for load computation

present the idea of finding a surrogate surface.

present the algorithm for computing the load on control volume boundaries.derive the formulas.

present the conservation and consistency properties.


CHAPTER 5. INTERFACE TREATMENT 14

5.3.3 Numerical accuracy study

present the setup of the academic problem where the fluid pressure field ispre-specified.

provide the error plot. show the order of accuracy for the two load computationmethods.

Chapter 6

Applications

6.1 Applications in aeronautics

6.1.1 Verification for a steady flow around an aircraft wing

for HALE flights

compare the steady-state solutions of body-fitted and embedded.

compare the computational cost of body-fitted and embedded. should be aboutthe same.

6.1.2 Verification for a transient flow past a heaving AGARD

wing

compare the history of lift obtained from embedded and body-fitted.

compare the computational cost of embedded and body-fitted.

6.1.3 Application to the fluid-structure interaction problem

with ultra-thin flapping wings

mention the challenges of this problem.

15

CHAPTER 6. APPLICATIONS 16

show the fluid and structure solutions at different time instances. mention thelarge structural deformation.

6.2 Applications in underwater implosion and ex-

plosion

6.2.1 Validation for the implosive collapse of an air-backed

aluminum cylinder submerged in water (IMP69)

describe the experiment and the challenges for numerical simulation.

present the simulation setup for the shell model.

show fluid results using different EOS (Tait and Stiffened Gas) they are similar.Use stiffened gas for the rest of this section.

show convergence in space using two different CFD grids.

show convergence in time using two (or more) different time-steps.

compare experimental and simulation results at two sensors.

present the hybrid model for the shell.

compare the shape of the collapsed cylinder from the dry/coupled simulations.

compare experimental and simulation results at two sensors.

6.2.2 Application to the explosion-driven fracture propaga-

tion of an air-backed aluminum cylinder submerged in

water.

describe the setup of the simulation and the challenges (multi-phase FSI w/cracking).

CHAPTER 6. APPLICATIONS 17

show the simulation results of (1) structural deformation; (2) fluid pressure; (3)fluid-structure and fluid-fluid interfaces at different time instances.

6.3 Application in gaseous detonation

describe the setup of the Shepherd experiment.

present the simulation setup and fluid/structure solutions.

compare the shape of the deformed/cracked pipe in the experiment and thesimulation

compare the fluid pressure (at a sensor location) obtained from the experimentand from the simulation.

Chapter 7

Conclusions and Perspectives for

Future Work

18

Kevin Guanyuan Wang

I certify that I have read this dissertation and that, in my opinion, it

is fully adequate in scope and quality as a dissertation for the degree

of Doctor of Philosophy.

(Charbel Farhat) Principal Adviser




(Adrian Lew)




(Gianluca Iaccarino)

Approved for the University Committee on Graduate Studies

kevin thesis draft

Documents

fluid model

fluid riemann problems52

phase fluid riemann

structure model42

numerical algorithm

numerical accuracy study

numerical methods

numerical examples