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Introduction to 3+1 Numerical Relativity$
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Miguel Alcubierre

Print publication date: 2008

Print ISBN-13: 9780199205677

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199205677.001.0001

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Introduction to 3+1 Numerical Relativity

Miguel Alcubierre

Oxford University Press

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 some simple equations of state. It also discusses the hyperbolicity properties of the hydrodynamic system of evolution equations, the concept of weak solutions and shock waves, and how to generalize the Euler equations to the case of imperfect fluids with heat conduction and viscosity.

Keywords:   Euler equations, equations of state, hydrodynamic equations, hyperbolicity, Riemann problem, imperfect fluids, irreversible thermodynamics

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