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Linear and Nonlinear Hydrodynamic Waves

Luciano Rezzolla and Olindo Zanotti

in Relativistic Hydrodynamics

Published in print:
2013
Published Online:
January 2014
ISBN:
9780198528906
eISBN:
9780191746505
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528906.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter is devoted to the conditions under which nonlinear hydrodynamical waves are produced and to the study of the flow properties across such waves. Special emphasis is given to the ... More


RELATIVISTIC HYDRODYNAMICS

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the derivation of dynamical equations governing the motion of a perfect fluid, known as the Euler equations, both in the special and general relativistic cases. It considers ... More


The Finite-Volume Method

Heiner Igel

in Computational Seismology: A Practical Introduction

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198717409
eISBN:
9780191835070
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198717409.003.0008
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The finite-volume method is introduced as a consequence of a general (mass, tracer, energy) conservation problem. The wave equation is derived from this fundamental conservation principle. The ... More


The Discontinuous Galerkin Method

Heiner Igel

in Computational Seismology: A Practical Introduction

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198717409
eISBN:
9780191835070
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198717409.003.0009
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the ... More


Shocks

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0006
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

When the speed of a fluid exceeds that of sound, discontinuities in density occur, called shocks.The opposite limit from incompressibility (constant density) is constant pressure. In this limit, we ... More


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