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Consistent explicit staggered schemes for compressible flows Part I: the barotropic Euler equations.

机译:可压缩流的一致显式交错方案第一部分:正压欧拉方程。

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摘要

In this paper, we build and analyze the stability and consistency of an explicit scheme for the compressible barotropic Euler equations. This scheme is based on a staggered space discretization, with an upwinding performed with respect to the material velocity only (so that, in particular, the pressure gradient term is centered). The velocity convection term is built in such a way that the solutions satisfy a discrete kinetic energy balance, with a remainder term at the left-hand side which is shown to be non-negative under a CFL condition. Then, in one space dimension, we prove that if the solutions to the scheme converge to some limit as the time and space step tend to zero, then this limit is an entropy weak solution of the continuous problem. Numerical tests confirm this theory, and show in addition (in 1D, and thus in absence of contact discontinuities) a first-order convergence rate.
机译:在本文中,我们建立并分析了可压缩正压欧拉方程的一个显式格式的稳定性和一致性。该方案基于交错的空间离散,其中仅相对于材料速度执行上风(因此,尤其是使压力梯度项居中)。速度对流项以这样的方式建立:解满足离散的动能平衡,其余项在左侧,在CFL条件下显示为非负。然后,在一个空间维度上,我们证明如果随着时间和空间步长趋于零,该方案的解收敛到某个极限,则该极限是连续问题的熵弱解。数值测试证实了这一理论,并且另外(在一维中,因此在没有接触间断的情况下)显示出一阶收敛速度。

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