标题： 计算超相对论欧拉方程的径向对称解的熵稳定不连续伽辽金方法 显示英文标题

标题： Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods

摘要： 超相对论欧拉方程描述了在热能占主导地位的相对论情况下的气体。 对于理想气体，这些方程是用压力、无量纲四速度的空间部分和粒子密度来表示的。 Kunik 等人（2024，https://doi.org/10.1016/j.jcp.2024.113330）为超相对论欧拉方程提出了真正的多维基准问题。 特别是，他们将径向对称问题的全二维不连续伽辽金模拟与使用特定一维方案计算的解进行了比较。 解中特别值得关注的是激波的形成和压力爆炸。 在本工作中，我们推导了超相对论欧拉方程的熵稳定通量。 因此，我们推导了主场（或熵变量）及其相应的势能。 然后，我们提出熵稳定通量，并以不同测试案例的二维和三维模拟结果结束。 显示英文摘要

摘要： The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and the particle density. Kunik et al.\ (2024, https://doi.org/10.1016/j.jcp.2024.113330) proposed genuine multi--dimensional benchmark problems for the ultra--relativistic Euler equations. In particular, they compared full two-dimensional discontinuous Galerkin simulations for radially symmetric problems with solutions computed using a specific one-dimensional scheme. Of particular interest in the solutions are the formation of shock waves and a pressure blow-up. In the present work we derive an entropy-stable flux for the ultra--relativistic Euler equations. Therefore, we derive the main field (or entropy variables) and the corresponding potentials. We then present the entropy-stable flux and conclude with simulation results for different test cases both in 2D and in 3D.