CONTENTS -- Foreword -- Preface -- An Introduction to the Immersed Boundary and the Immersed Interface Methods Robert H. Dillon and Zhilin Li -- 1. Introduction -- Part I AN INTRODUCTION TO THE IMMERSED BOUNDARY METHOD -- 2. Overview of Immersed Boundary Method -- 3. Some Applications of the IB Method -- 4. Some Technical Issues of the IB Method -- Part II A TUTORIAL OF THE IMMERSED INTERFACE METHOD -- 5. The Immersed Interface Method for Elliptic Interface Problems -- 5.1. The IIM for 1D elliptic interface problems -- 5.2. The immersed interface method for 2D elliptic interface problems -- 5.3. Some issues for three-dimensional problems -- 6. The Augmented Immersed Interface Method and Applications -- 6.1. The augmented immersed interface method for Poisson equations on irregular domains -- 6.2. The augmented immersed interface method for the incompressible two-phase .ow problem -- 7. Simplifying the Immersed Interface Method by Removing Source Singularities -- 8. The Immersed Interface Method Using Finite Element Formulations -- 8.1. The modified basis functions for one-dimensional problems -- 8.2. Modified basis functions for two-dimensional problems -- 9. The IIM for Free Boundary or Moving Interface Problems -- 10. Acknowledgements -- References -- 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 -- 0. Introduction -- 1. Tumor Growth in Homogeneous Tissuea -- 1.1. Overview -- 1.2. Discrete modeling -- 1.3. Continuum modeling -- 1.4. Regimes of growth -- 1.5. Comparison with experiment -- 1.6. Linear analysis -- 1.7. Nonlinear results -- 2. Tumor Growth in Heterogeneous Tissueb -- 2.1. Overview -- 2.2. Governing equations -- 2.3. Nonlinear results -- 3. Tumor Growth and Neovascularizationc.

3.1. Overview -- 3.2. The model -- 3.3. Nonlinear results -- 4. Conclusion and Future Research Directions -- References -- Progress in Modeling Pulsed Detonations Frank K. Lu and R. Bellini -- 1. Introduction and Literature Review -- 2. Overview of Early Studies in Detonations -- 2.1. Structure of detonation waves -- 3. Review of Numerical Simulation of Pulse Detonation Engines -- 3.1. Detonation initiation -- 3.2. Detonation stability -- 3.3. Numerics and algorithms -- 3.4. Boundary conditions -- 3.5. Turbulence modeling -- 3.6. Chemical kinetics -- 4. The Governing Equations -- 5. Numerical Method -- 5.1. Local ignition averaging method -- 6. Numerical Simulations of Pulse Detonations -- 6.1. One-dimensional detonation wave propagation -- 6.2. Detonation wave propagation through an area enlargement -- 7. Outlook and Conclusions -- Acknowledgments -- References -- Direct Numerical Simulations of Multiphase Flows Gr etar Tryggvason and Jiacai Lu -- 1. Introduction -- 2. Governing Equations -- 3. Numerical Method -- 4. Results -- 5. Conclusions -- Acknowledgments -- References.