Numerical study of non-uniqueness for 2D compressible isentropic Euler equations.
Numerical study of non-uniqueness for 2D compressible isentropic Euler equations.
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二维可压缩等熵欧拉方程非唯一性的数值研究。
DOI：
10.1016/j.jcp.2021.110588
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发表时间：
2021
影响因子：
4.1
通讯作者：
and Liu, Hailiang
中科院分区：
文献类型：
--
作者：
Bressan, Alberto;Jiang, Yi;and Liu, Hailiang
在本文中，我们数值研究了一类解的螺旋奇异涡的二维，无粘，可压缩欧拉系统，其中的初始数据有一个代数奇异涡在原点。这些都不同于文献中广泛研究的多维黎曼问题。我们的计算提供了数值证据的存在多个解决方案的初始值问题，从而揭示了一个根本的障碍对适定性的控制方程。采用保正间断Galerkin方法求解可压缩Euler方程。
In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin. These are different from the multi-dimensional Riemann problems widely studied in the literature. Our computations provide numerical evidence of the existence of initial value problems with multiple solutions, thus revealing a fundamental obstruction toward the well-posedness of the governing equations. The compressible Euler equations are solved using the positivity-preserving discontinuous Galerkin method.