论文标题
一类线性隐式方案的渐近性特性，用于弱压缩的Euler方程
Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
论文作者
论文摘要
在本文中，我们得出并分析了一类线性隐式方案，其中包括Feistauer和Kučera之一（JCP 2007）以及RS-EMEX方案类。隐式部分基于在参考状态下评估的雅各布矩阵。如Feistauer和Kučera（JCP 2007），该状态可以是旧时间水平的解决方案，也可以是不可压缩极限方程的数值近似，如Zeifang等人。 （Commun。Comput。Phys。2009），或可能是另一种状态。随后，结果表明，在离散的希尔伯特扩张的假设下，这种类别的方法是渐近地保存的。对于一维设置，对参考状态有一定的限制，显示了离散的希尔伯特膨胀的存在。
In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (JCP 2007) as well as the class of RS-IMEX schemes. The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (JCP 2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun. Comput. Phys. 2009), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.
