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Relativistic numerical hydrodynamics. (English) Zbl 1095.83003
Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press (ISBN 0-521-63155-6/hbk). xvi, 216 p. (2003).
This book is aimed to cover relativistic numerical hydrodynamics, but it is useful also for those researchers not directly interested in the numerical methods involved. In fact, already the 20 pages introduction is a nice presentation of relativity, the properties of the matter tensor and the ADM-metric, useful also for a general context.
Each of the 7 chapters has its own reference list, the headings of them are: 1. Introduction, 2. Special relativistic hydrodynamics, 3. General relativistic hydrodynamics, 4. Cosmological hydrodynamics, 5. Stellar collapse and supernovae, 6. Axially symmetric relativistic hydrodynamics, 7. Hydrodynamics in three spatial dimensions.
The general style of the book is to explain the physics, give the formulas, and then to show the peculiarities for a numerical implementation of the problem accompanied by figures as outcome of the numerics.

MSC:
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83A05 Special relativity
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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