Finite volume method for the relativistic burgers model on a (1+1)-Dimensional de sitter spacetime

Download
2016-05-10
Ceylan, Tuba
Okutmuştur, Baver
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 cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves.
Mathematical and Computational Applications

Suggestions

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...
Derivation of the relativistic burgers equation on a de sitter background
Okutmuştur, Baver (null; 2014-12-17)
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–Lemaˆıt...
Reisnerr-Nordstrom Spacetime Geometry: Derivation of the Euler and Burgers Models
Okutmuştur, Baver (2018-7-07)
A relativistic generalization of the Euler and Burgers models have recently been introduced and analyzed both theoretically and numerically. In this work we extend these analysis to a particular type of the Lorentzian manifold, so called the Reissnerr-Nordström (RS) spacetime geometry. We introduce basic properties of the R-S spacetime and its metric components containing electrical charge term which distinguish the R-S spacetime from the Schwarzshild geometry. Furthermore, we present a derivation of the Eu...
Relativistic Burgers Models on Curved Background Geometries
Okutmuştur, Baver (Springer-Verlag, 2019-01-01)
Relativistic Burgers model and its generalization to various spacetime geometries are recently studied both theoretically and numerically. The numeric implementation is based on finite volume and finite difference approximation techniques designed for the corresponding model on the related geometry. In this work, we provide a summaryof several versions of these models on the Schwarzschild, de Sitter, Schwarzschild-de Sitter, FLRW and Reissner-Nordstr¨om spacetime geometries with their particular properties.
Finite mass gravitating Yang monopoles
CEBECİ, HAKAN; Sarıoğlu, Bahtiyar Özgür; Tekin, Bayram (American Physical Society (APS), 2008-12-01)
We show that gravity cures the infrared divergence of the Yang monopole when a proper definition of conserved quantities in curved backgrounds is used, i.e. the gravitating Yang monopole in cosmological Einstein theory has a finite mass in generic even dimensions (including time). In addition, we find exact Yang-monopole type solutions in the cosmological Einstein-Gauss-Bonnet-Yang-Mills theory and briefly discuss their properties.
Citation Formats
T. Ceylan and B. Okutmuştur, “Finite volume method for the relativistic burgers model on a (1+1)-Dimensional de sitter spacetime,” Mathematical and Computational Applications, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46047.