论文标题
2D可压缩等电欧方程的非独立性的数值研究
Numerical Study of Non-uniqueness for 2D Compressible Isentropic Euler Equations
论文作者
论文摘要
在本文中，我们从数值上研究了一类旋转旋转性的解决方案，用于二维，无情，可压缩的Euler系统，在该系统中，初始数据的原始数据具有代数奇异性。这些不同于文献中广泛研究的多维Riemann问题。我们的计算提供了数值证据表明，具有多种解决方案存在初始价值问题，从而揭示了对理事方程式良好的基本障碍。可压缩的Euler方程是使用保留阳性的不连续的Galerkin方法来求解的。
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.
