Derivation of the relativistic burgers equation on a de sitter background

Date

2014-12-17

Author

Okutmuştur, Baver

Metadata

Show full item record

Item Usage Stats

240
views

0
downloads

Recently several versions of relativistic Burgers equations have been derived on different spacetime geometries by the help of Lorentz invariance property and the Euler system of relativistic compressible flows on the related backgrounds. The concerning equations on Minkowski (flat) and Schwarzshild spacetimes are obtained in the article [6] where the finite volume approximations and numerical calculations of the given models are presented in detail. On the other hand a similar work on the Friedmann–Lemaˆıtre–Robertson–Walker (FLRW) geometry is described in [3]. In this paper, we consider a family member of FLRW spacetime so-called de Sitter background, introduce some important features of this spacetime with its metric and derive the relativistic Burgers equation on it. The Euler system of equations on de Sitter spacetime can be found by a known process by the help of Christoffel symbols and tensors for perfect fluids. We applied the usual techniques used in [3, 6] to derive relativistic Burgers equations from the Euler system on de Sitter background. By the help of finite volume method on curved spacetimes, we examined the numerical illustrations of the given model in the last part.

Subject Keywords

Relativistic Burgers equations, De Sitter metric, Euler system, Spacetime, Finite volume approximation

URI

http://www.wseas.us/e-library/conferences/2014/Istanbul/AMATH/AMATH-00.pdf
https://hdl.handle.net/11511/77730

Conference Name

International Conference on Applied Mathematics, Mathematics and Computers in Science and Engineering Series, (15 - 17 Aralık 2014)

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Finite volume method for the relativistic burgers model on a (1+1)-Dimensional de sitter spacetime Ceylan, Tuba; Okutmuştur, Baver (2016-05-10) Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cos...
Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime Ceylan, Tuba; Okutmuştur, Baver (2017-01-01) The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive there lativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constantis also taken i...
RELATIVISTIC BURGERS EQUATIONS ON CURVED SPACETIMES. DERIVATION AND FINITE VOLUME APPROXIMATION Lefloch, Philippe G.; Makhlof, Hasan; Okutmuştur, Baver (2012-01-01) Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler equations of relativistic compressible fluids. This model is unique up to normalization and converges to the standard inviscid Burgers equation in the limit of infinite light speed. Furthermore, from the Euler system of relativistic compressible flows on a curved background, we d...
Parallel processing of two-dimensional euler equations for compressible flows Doǧru, K.; Aksel, M.h.; Tuncer, İsmail Hakkı (2008-12-01) A parallel implementation of a previously developed finite volume algorithm for the solution of two-dimensional, unsteady, compressible Euler equations is given. The conservative form of the Euler equations is discretized with a second order accurate, one-step Lax-Wendroff scheme. Local time stepping is utilized in order to accelerate the convergence. For the parallel implementation of the method, the solution domain is partitioned into a number of subdomains to be distributed to separate processors for par...
On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems AKBAŞ, MERAL; Kaya, Serap; Kaya Merdan, Songül (2017-07-01) We prove long-time stability of linearly extrapolated BDF2 (BDF2LE) timestepping methods, together with finite element spatial discretizations, for incompressible Navier-Stokes equations (NSE) and related multiphysics problems. For the NSE, Boussinesq, and magnetohydrodynamics schemes, we prove unconditional long time L-2 stability, provided external forces (and sources) are uniformly bounded in time. We also provide numerical experiments to compare stability of BDF2LE to linearly extrapolated Crank-Nicolso...

Citation Formats

B. Okutmuştur, “Derivation of the relativistic burgers equation on a de sitter background,” İstanbul, Türkiye, 2014, vol. 38, p. 41, Accessed: 00, 2021. [Online]. Available: http://www.wseas.us/e-library/conferences/2014/Istanbul/AMATH/AMATH-00.pdf.