Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime

Ceylan, Tuba
Okutmuştur, Baver
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 into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments.


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...
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...
Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients
Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005)
In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
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...
Citation Formats
T. Ceylan and B. Okutmuştur, “Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime,” TURKISH JOURNAL OF MATHEMATICS, pp. 1027–1041, 2017, Accessed: 00, 2020. [Online]. Available: