Physics and Ecology in Fluids
Modeling and Numerical Experiments
- 1st Edition - February 1, 2023
- Imprint: Elsevier
- Authors: Marek Stastna, Derek Steinmoeller
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 0 4 9 1 - 9
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 1 4 6 1 - 1
Physics and Ecology in Fluids: Modeling and Numerical Experiments develops mathematical and numerical modeling methodologies for coupled biological-hydrodynamic problems with a fo… Read more
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Request a sales quotePhysics and Ecology in Fluids: Modeling and Numerical Experiments develops mathematical and numerical modeling methodologies for coupled biological-hydrodynamic problems with a focus on process studies. The modeling is presented in a way that discusses mathematical background but does not depend on a large body of mathematical pre-requisites or experience. Models are built up from simple, to complex. This includes discussion of approximations and shortcuts commonly made by large computational models for natural bodies of water. Computational approaches are presented using conceptual explanations and pseudo-code along with well-documented, open-source code. Over a dozen codes that run locally on the reader’s laptop provide hands on experience with various aspects of the modeling process and its scientific results. One large-scale code for basin scale modeling based on the Discontinuous Galerkin methodology is presented, along with a self-contained discussion of theoretical background and implementation details.
Physics and Ecology in Fluids is written for graduate students, academic researchers and government scientists. Professors can use the book as a stand-alone resource for a one term graduate course, or to supplement teaching of their own graduate courses. All readers may also use the book as background/user’s guide for the software included with the book.
- Presents accessible codes along with clear explanations of the mathematical modeling process that leads up to the code
- Provides a consistent development of the mathematical models for hydrodynamic and biological modeling, which are rarely covered together
- Includes an informal, discussion-style tone throughout, but with serious applied mathematics content, allowing a level of detail relevant for multiple reader types
Researchers, Professors and students in Physical limnologists and coastal oceanographers. Researchers, Professors and students in Applied mathematics
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- List of figures
- List of tables
- List of source code files
- Preface
- Acknowledgments
- Chapter 1: Introductory remarks and reader's guide
- Abstract
- 1.1. Introduction
- 1.2. Reader's guide
- References
- Chapter 2: The basics of modeling: Mechanics and population models
- Abstract
- 2.1. A (not so) basic model
- 2.2. Exponential growth
- 2.3. Logistic growth
- 2.4. The Lotka-Volterra model
- 2.5. Extending the Lotka-Volterra model
- 2.6. Models of plankton populations
- 2.7. Mini-projects
- 2.8. Computing spectra
- References
- Chapter 3: Modeling active tracers
- Abstract
- 3.1. Numerical experiments
- 3.2. Active tracers: the simplest models
- 3.3. Nonlinear effects
- 3.4. Interacting tracers: the Lotka-Volterra model
- 3.5. Advection-diffusion for plankton models
- 3.6. Tracers in two dimensions
- 3.7. Advection diffusion population model in 2D
- 3.8. Mini-projects
- References
- Chapter 4: Fluid mechanics
- Abstract
- 4.1. The basics of fluid mechanics: accounting for flow
- 4.2. Forces in a fluid: generalizing Newton's second law
- 4.3. The shallow water equations
- 4.4. Vorticity and stream function
- 4.5. Mini-projects
- References
- Chapter 5: Rotating shallow water dynamics: An overview
- Abstract
- 5.1. An overview of material
- 5.2. The effect of rotation: geostrophy
- 5.3. Rotating gravity waves in a channel: derivation
- 5.4. Rotating gravity waves in a channel: discussion
- 5.5. The circular lake: derivation
- 5.6. The circular lake: discussion
- 5.7. The tilted free surface problem
- 5.8. An instability problem: simulation
- 5.9. Mini-projects
- References
- Chapter 6: Rotating shallow water dynamics: Dispersion and nonlinearity
- Abstract
- 6.1. Realism in wave models
- 6.2. The dispersive shallow water model
- 6.3. Adjustment problems on the field scale
- 6.4. Seiche evolution
- 6.5. Coding ideas
- 6.6. Mini-projects
- References
- Chapter 7: Understanding complex dynamics in two and three dimensions
- Abstract
- 7.1. Turbulence closures: the idea
- 7.2. Turbulence closures: Navier Stokes
- 7.3. Large-eddy simulations (or LES)
- 7.4. Slow-fast systems
- 7.5. Mini-projects
- References
- Chapter 8: Modeling motion in the vertical
- Abstract
- 8.1. Stratified fluid dynamics in the x-z plane
- 8.2. The idealized internal seiche: derivation
- 8.3. The idealized internal seiche: transport
- 8.4. The internal seiche: arbitrary stratifications
- 8.5. The internal seiche: finite amplitude and wavetrains
- 8.6. Nonlinearity due to biological behavior
- 8.7. Mini-projects
- References
- Chapter 9: Modeling fluid transport processes with finite volume methods
- Abstract
- 9.1. Beyond spectral methods
- 9.2. A short history of finite volume methods
- 9.3. Getting acquainted with finite volume methods in 1D
- 9.4. Insight from 1D energy analysis: the continuous problem
- 9.5. Insight from 1D energy analysis: the discrete problem
- 9.6. Exercises: building intuition
- 9.7. Implementation details in 1D
- 9.8. Doing it “the right way” in 2D
- 9.9. Towards harder problems
- 9.10. Well-balanced upwinding for the case of variable bottom bathymetry
- 9.11. Returning to the dispersive shallow water system
- 9.12. Towards “high-resolution” numerical schemes
- 9.13. Wrap-up
- 9.14. Mini-projects
- References
- Chapter 10: Modeling fluid transport processes with discontinuous Galerkin methods: Background
- Abstract
- 10.1. An overview of material
- 10.2. Discontinuous Galerkin finite element method for dispersive shallow water equations
- 10.3. Evaluating the inner products: modes and nodes
- 10.4. Polynomial interpolation nodes in 2D
- 10.5. Local operators for the nodal approach
- 10.6. Surface integral contributions
- 10.7. Boundary conditions
- 10.8. Dealing with source terms: bathymetry and wave dispersion
- 10.9. Solving for the non-hydrostatic pressure: an elliptic problem
- 10.10. Hyperbolic theory in 1D
- 10.11. Linear Riemann problem
- 10.12. Time-stepping method
- 10.13. Mini-projects
- References
- Chapter 11: Modeling fluid transport processes with discontinuous Galerkin methods: Implementation
- Abstract
- 11.1. Towards practical implementations of DG-FEM
- 11.2. Spurious eddies in inviscid DG-FEM solutions
- 11.3. Curvilinear elements
- 11.4. Constructing coordinates systems for curvilinear elements
- 11.5. Cubature and quadrature integration
- 11.6. Internal rotating seiche simulation using curvilinear elements
- 11.7. Internal rotating seiche simulation in a real-world lake
- 11.8. Wrap-up
- References
- Chapter 12: Beyond standard treatments: Flow in porous media
- Abstract
- 12.1. Motivation
- 12.2. The basic theory of porous media
- 12.3. Flow in saturated porous media: two simple examples
- 12.4. Flow in saturated porous media: a more complex example
- 12.5. Towards more general descriptions: unsaturated flow
- 12.6. Mini-projects
- 12.7. Concluding remarks
- References
- Glossary
- Index
- Edition: 1
- Published: February 1, 2023
- Imprint: Elsevier
- No. of pages: 280
- Language: English
- Paperback ISBN: 9780323904919
- eBook ISBN: 9780323914611
MS
Marek Stastna
Marek Stastna is a professor in the mathematics department at the University of Waterloo. His primary research interest is the motion of stratified fluid mechanics, such as lakes, the coastal ocean and the atmosphere. He is part of the Environmental and Geophysical Fluid Mechanics group. He works on the simulation of stratified, natural waters. This includes fundamental work on hydrodynamics instabilities, bottom boundary layers and mixing, as well as more applied work on lake scale circulation. Professor Stastna has been actively involved in the building of several numerical models, using pseudospectral and finite element methodologies. He has published numerous articles and book chapters.
Affiliations and expertise
Professor, Mathematics Department, University of Waterloo, CanadaDS
Derek Steinmoeller
Derek Steinmoeller is a Scientist and Senior Software Developer at Aquanty. His main interests lie in numerical solutions of equations of fluid flow in lakes under the effects of rotation, density stratification, and weak vertical accelerations. He is also a full-time senior software developer in a technology hub located in Waterloo region, Canada with more than six years of employment. He has experience in both traditional numerical modelling software, and more modern software architecture and design patterns in monolithic web applications that lay the groundwork for writing robust and maintainable code for any application area. He Developed an open-source suite of mathematical model solvers for a variety of application areas to be run on High-Performance Computing architectures.
Affiliations and expertise
Scientist and Senior Software Developer, Aquanty, CanadaRead Physics and Ecology in Fluids on ScienceDirect