Abstract Motivated by the work of Karper [29], we propose a numerical scheme to compressible Navier-Stokes system in spatial multi-dimension based on finite differences. The backward Euler method is applied for the time discretization, while a staggered grid, with continuity and momentum equations on different grids, is used in space. The existence of a solution to the implicit nonlinear scheme, strictly positivity of the numerical density, stability and consistency of the method for the whole range of physically relevant adiabatic exponents are proved. The theoretical part is complemented by computational results that are performed in two spatial dimensions.

中文翻译：

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多维可压缩粘性等熵流有限差分格式的稳定性和一致性

摘要 受 Karper [29] 工作的启发，我们提出了一种基于有限差分的空间多维可压缩 Navier-Stokes 系统的数值方案。时间离散采用后向欧拉法，空间采用交错网格，在不同网格上具有连续性和动量方程。证明了隐式非线性方案的解的存在性、数值密度的严格正性、该方法在整个物理相关绝热指数范围内的稳定性和一致性。理论部分由在两个空间维度中执行的计算结果补充。