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Flows of Viscous Incompressible Fluids

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Fluid mechanics is concerned with the motion of gases and liquids and their interaction with the surroundings. A fluid can either be inviscid (the viscosity is assumed to be zero) or incompressible ... 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.


Material Nonlinearities and Coupled Problems

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and ... More


Nonlinear Analysis of Time-Dependent Problems

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, finite element models are used to solve time-dependent problems with nonlinearities and some standard time approximation schemes are described. All classes of nonlinear problems ... More


Fluid Kinematics

David Jon Furbish

in Fluid Physics in Geology: An Introduction to Fluid Motions on Earth's Surface and Within its Crust

Published in print:
1997
Published Online:
November 2020
ISBN:
9780195077018
eISBN:
9780197560358
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195077018.003.0011
Subject:
Earth Sciences and Geography, Geophysics: Earth Sciences

Let us momentarily recall an elementary problem from physics: describing the motion of a ballistic particle. To do this in a formal way first required developing ... More


Two-Dimensional and Geophysical Fluid Mechanics

A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo

in Physics of Long-Range Interacting Systems

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199581931
eISBN:
9780191787140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199581931.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this Chapter the statistical mechanics theory of long-range interactions is applied to hydrodynamics problems. The Euler equation is derived as a limiting case of the two dimensional Navier-Stokes ... More


Basic Concepts

Eric B. Kraus and Joost A. Businger

in Atmosphere-Ocean Interaction

Published in print:
1995
Published Online:
November 2020
ISBN:
9780195066180
eISBN:
9780197560204
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195066180.003.0005
Subject:
Earth Sciences and Geography, Oceanography and Hydrology

Both Cartesian tensor and vector notation will be used in this text. The notation xi means the i-component of the vector x = (x1 x2, x3). When used in the argument of ... More


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