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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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