INTERFACE PROBLEMS AND METHODS IN BIOLOGICAL AND PHYSICAL FLOWS (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore)

This volume showcases lecture notes collected from tutorials presented at the Workshop on Moving Interface Problems and Applications in Fluid Dynamics that was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences, National University of Singapore. As part of the program, these tutorials were conducted by specialists within their respective areas such as Robert Dillon, Zhilin Li, John Lowengrub, Frank Lu and Gretar Tryggvason. The topics in the program encompass modeling and simulations of biological flow coupled to deformable tissue/elastic structure, shock wave and bubble dynamics and various applications like biological treatments with experimental verification, multi-medium flow or multiphase flow and various applications including cavitation/supercavitation, detonation problems, Newtonian and non-Newtonian fluid, and many other areas. This volume benefits graduate students and researchers keen in the field of interfacial flows for application to physical and biological systems. Even beginners will find this volume a very useful starting point with many relevant references applicable. CONTENTS......Page 9 Foreword......Page 6 Preface......Page 7 An Introduction to the Immersed Boundary and the Immersed Interface Methods Robert H. Dillon and Zhilin Li......Page 10 1. Introduction......Page 11 2. Overview of Immersed Boundary Method......Page 12 3. Some Applications of the IB Method......Page 17 4. Some Technical Issues of the IB Method......Page 25 Part II A TUTORIAL OF THE IMMERSED INTERFACE METHOD......Page 27 5.1. The IIM for 1D elliptic interface problems......Page 28 5.2. The immersed interface method for 2D elliptic interface problems......Page 32 5.3. Some issues for three-dimensional problems......Page 40 6. The Augmented Immersed Interface Method and Applications......Page 42 6.1. The augmented immersed interface method for Poisson equations on irregular domains......Page 45 6.2. The augmented immersed interface method for the incompressible two-phase .ow problem......Page 46 7. Simplifying the Immersed Interface Method by Removing Source Singularities......Page 50 8. The Immersed Interface Method Using Finite Element Formulations......Page 53 8.1. The modified basis functions for one-dimensional problems......Page 54 8.2. Modified basis functions for two-dimensional problems......Page 55 9. The IIM for Free Boundary or Moving Interface Problems......Page 57 10. Acknowledgements......Page 65 References......Page 66 Lecture Notes on Nonlinear Tumor Growth: Modeling and Simulation John S. Lowengrub, Vittorio Cristini, Hermann B. Frieboes, Xiangrong Li, Paul Macklin, Sandeep Sanga, Steven M. Wise and Xiaoming Zheng......Page 78 0. Introduction......Page 79 1.1. Overview......Page 81 1.2. Discrete modeling......Page 82 1.3. Continuum modeling......Page 84 1.4. Regimes of growth......Page 87 1.5. Comparison with experiment......Page 89 1.6. Linear analysis......Page 90 1.7. Nonlinear results......Page 93 2.2. Governing equations......Page 102 2.3. Nonlinear results......Page 106 3.1. Overview......Page 116 3.2. The model......Page 119 3.3. Nonlinear results......Page 121 4. Conclusion and Future Research Directions......Page 127 References......Page 131 1. Introduction and Literature Review......Page 144 2. Overview of Early Studies in Detonations......Page 145 2.1. Structure of detonation waves......Page 148 3. Review of Numerical Simulation of Pulse Detonation Engines......Page 150 3.2. Detonation stability......Page 151 3.3. Numerics and algorithms......Page 153 3.5. Turbulence modeling......Page 154 3.6. Chemical kinetics......Page 155 4. The Governing Equations......Page 156 5. Numerical Method......Page 157 5.1. Local ignition averaging method......Page 158 6. Numerical Simulations of Pulse Detonations......Page 160 6.1. One-dimensional detonation wave propagation......Page 161 6.2. Detonation wave propagation through an area enlargement......Page 162 7. Outlook and Conclusions......Page 163 Acknowledgments......Page 164 References......Page 165 1. Introduction......Page 170 2. Governing Equations......Page 172 3. Numerical Method......Page 174 4. Results......Page 178 5. Conclusions......Page 182 References......Page 183

This volume showcases lecture notes collected from tutorials presented at the Workshop on Moving Interface Problems and Applications in Fluid Dynamics that was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences, National University of Singapore. As part of the program, these tutorials were conducted by specialists within their respective areas.

An introduction to the immersed boundary and the immersed interface methods / Robert H. Dillon and Zhilin Li -- Lecture notes on nonlinear tumor growth: modeling and simulation / John S. Lowengrub [und weitere] -- Progress in modeling pulsed detonations / Frank K. Lu and R. Bellini -- Direct numerical simulations of multiphase flows / Grétar Tryggvason and Jiacai Lu