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Seminars»12.12.2013 - Baver Okutmustur : Derivation of relativistic and non-relativistic Burgers equations on a curved spacetime

12.12.2013 - Baver Okutmustur : Derivation of relativistic and non-relativistic Burgers equations on a curved spacetime

Derivation of relativistic and non-relativistic Burgers equations on a curved spacetime

Baver Okutmustur
Mathematics Dept., METU
12 December 2013, Thursday, 14:40
Cavid Erginsoy Seminar Room, Physics Department, 3rd floor

Abstract: The Burgers equation is an important model in computational fluid dynamics,which can be formally derived from the Euler equations of compressible fluids.It is also the simplest example of nonlinear hyperbolic conservation law and has played an essential role in the development of robust and accurate, shock capturing schemes for the approximation of entropy solutions to nonlinear hyperbolic systems. Recently, several relativistic and non-relativistic generalizations of Burgers equation have been derived and furthermore, a finite volume scheme for the approximation of discontinuous solutions to these equations has been introduced ((:cell PQA(PSS(2):), (:cell PQA(PSS(3):)). In this talk, a comparison of the derived Burgers equations in both relativistic and non-relativistic cases will be formulated depending on the background geometry which is supposed to be a curved spacetime. By imposing the pressure to be vanished, the proposed relativistic and non-relativistic equations are obtained from the Euler system of compressible flows. The related formulations and numerical studies have already been analyzed for (1+1-dimensional) Minkowski and Schwarzschild spacetimes, whereas the examination for Friedmann-Lemaitre-Robertson-Walker (FLRW) background is still in process.

References:

1 Ceylan T., , and Okutmustur B., Derivation of relativistic Burgers equations on Friedmann-Lemaitre-Robertson-Walker (FLRW) model and numerical experiments, in preparation.

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4 Smoller J., and Temple B., Global Solutions of the Relativistic Euler equations,Commun. Math. Phys., 156 67{99, (1993).

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