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## Boundaries and Geometries

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude ... More

## The Porous Medium Equation: Mathematical Theory

*Juan Luis Vazquez*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198569039
- eISBN:
- 9780191717468
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198569039.001.0001
- Subject:
- Mathematics, Mathematical Physics

The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it ... More

## A Model of Rayleigh-Bénard Convection

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, ... More

## Pattern Formation and Spatiotemporal Chaos

*Robert C. Hilborn*

### in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198507239
- eISBN:
- 9780191709340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507239.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

When a dynamical system has significant spatial extent, its nonlinear dynamics can lead to the spontaneous formation of spatial patterns. Such systems provide models for how nature might have ... More

## Fundamentals of fluid dynamics with an introduction to the importance of interfaces

*H. A. Stone*

### in Soft Interfaces: Lecture Notes of the Les Houches Summer School: Volume 98, July 2012

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780198789352
- eISBN:
- 9780191831201
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198789352.003.0001
- Subject:
- Physics, Soft Matter / Biological Physics

The topics discussed are all related to basic fluid mechanics. In these introductory notes I highlight some of the main features of fluid flows and their mathematical characterization. There is much ... More

## Introduction

*Bijan Mohammadi and Olivier Pironneau*

### in Applied Shape Optimization for Fluids

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0001
- Subject:
- Mathematics, Mathematical Physics

This is a general introduction with prospective issues. This book discusses shape optimization problems for fluids and presents the state of the art in shape optimization for an extended range of ... More

## Weak-Form Finite Element Models of Flows of Viscous Incompressible Fluids

*J. N. Reddy*

### in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

- Published in print:
- 2014
- Published Online:
- June 2015
- ISBN:
- 9780199641758
- eISBN:
- 9780191789557
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641758.003.0010
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter presents finite element models of flows of viscous incompressible fluids for Newtonian and non-Newtonian (power-law) fluids. It develops two different finite element models, namely, the ... More

## Models of Incompressible Fluid Flow

*Howard C. Elman, David J. Silvester, and Andrew J. Wathen*

### in Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199678792
- eISBN:
- 9780191780745
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199678792.003.0001
- Subject:
- Mathematics, Numerical Analysis, Computational Mathematics / Optimization

This preliminary chapter gives a brief introduction to the equations studied in depth in the book, as they are used to model incompressible fluids.

## Least-Squares Finite Element Models of Flows of Viscous Incompressible Fluids

*J. N. Reddy*

### in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

- Published in print:
- 2014
- Published Online:
- June 2015
- ISBN:
- 9780199641758
- eISBN:
- 9780191789557
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641758.003.0011
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter develops finite element formulations for flows of viscous incompressible fluids using high-order spectral/hp finite element technology and least-squares finite element formulation. The ... More

## Why a Kinetic Theory of Fluids?

*Sauro Succi*

### in The Lattice Boltzmann Equation: For Complex States of Flowing Matter

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780199592357
- eISBN:
- 9780191847967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199592357.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Fluid flows are a pervasive presence across most branches of human activity, including daily life. Although the basic equations governing the motion of fluid flows are known for two centuries (1822), ... More

## Hydrodynamics and black holes

*Yaron Oz*

### in Theoretical Physics to Face the Challenge of LHC: Lecture Notes of the Les Houches Summer School: Volume 97, August 2011

- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198727965
- eISBN:
- 9780191794278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198727965.003.0008
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter describes how the AdS/CFT correspondence (the Holographic Principle) relates field theory hydrodynamics to perturbations of black hole (brane) gravitational backgrounds. The ... More

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