TY - JOUR
T1 - A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime
JO - Communications in Computational Physics
VL - 2
SP - 500
EP - 519
PY - 2018
DA - 2018/02
SN - 23
DO - http://doi.org/10.4208/cicp.020415.260717a
UR - https://global-sci.org/intro/article_detail/cicp/10535.html
KW - Relativistic Burgers equation, FLRW metric, hyperbolic balance law, finite volume scheme.
AB - <p style="text-align: justify;">A relativistic generalization of the inviscid Burgers equation was introduced
by LeFloch and co-authors and was recently investigated numerically on a Schwarzschild
background. We extend this analysis to a Friedmann-Lemaître-Robertson-Walker
(FLRW) background, which is more challenging due to the existence of time-dependent,
spatially homogeneous solutions. We present a derivation of the model of interest
and we study its basic properties, including the class of spatially homogeneous solutions.
Then, we design a second-order accurate scheme based on the finite volume
methodology, which provides us with a tool for investigating the properties of solutions.
Computational experiments demonstrate the efficiency of the proposed scheme
for numerically capturing weak solutions.</p>