A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime
A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime
复制标题
DOI：
10.4208/cicp.020415.260717a
复制
发表时间：
2018
影响因子：
3.7
通讯作者：
Tuba Ceylan;P. LeFloch;Baver Okutmustur
中科院分区：
文献类型：
--
作者：
Tuba Ceylan;P. LeFloch;Baver Okutmustur
无粘性Burgers方程的相对论性推广是由LeFloch和合著者提出的，最近在Schwarzschild背景下进行了数值研究。我们将这一分析推广到Friedmann-Lemaı̂Tre-Robertson-Walker(FRW)背景，由于存在依赖时间的、空间齐次的解，因此更具挑战性。我们给出了兴趣模型的一种推导，并研究了它的基本性质，包括空间齐次解的类。然后，我们设计了一个基于有限体积法的二阶精度格式，为我们研究解的性质提供了一个工具。计算实验证明了该方法在数值捕捉弱解方面的有效性。AMS科目分类：35L65、76N10、83A05
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-Lemaı̂tre-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. AMS subject classifications: 35L65, 76N10, 83A05