Phys :
Seminars /
12.12.2013 - Baver Okutmustur : 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.

2 LeFloch P., Makhlof H., and Okutmustur B., Relativistic Burgers equations on a curved spacetime. Derivation and finite volume approximation, SIAM J. Numer. Anal. Vol. 50, No. 4, 2136{2158, (2012).

3 Amorim P., LeFloch P., and Okutmustur B., Finite Volume Schemes on Lorentzian Manifolds, Commun. Math. Sci. Vol. 6, No. 4, 1059-1086, (2008).

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

5 Russo G., and Khe A., High-order well-balanced schemes for systems of balance laws in Hyperbolic problems: theory, numerics and applications, Proc. Sympos. Appl., Vol. 67, Part 2, Amer. Math. Soc., 919-928, (2009).

(Printable View of http://www.physics.metu.edu.tr/Seminars/SEM13058)