In this paper we prove a convergence result for a discretization of the three-dimensional stationary compressible Navier–Stokes equations assuming an ideal gas pressure law |$p(\rho )=a \rho ^{\gamma }$| with |$\gamma> \frac{3}{2}$|⁠. It is the first convergence result for a numerical method with adiabatic exponents |$\gamma $| less than |$3$| when the space dimension is 3. The considered numerical scheme combines finite volume techniques for the convection with the Crouzeix–Raviart finite element for the diffusion. A linearized version of the scheme is implemented in the industrial software CALIF³S developed by the French Institut de Radioprotection et de Sûreté Nucléaire.

中文翻译：

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固定可压缩Navier-Stokes方程的收敛FV-FE格式

在本文中，我们证明了在理想气体压力定律| $ p（\ rho）= a \ rho ^ {\ gamma} $ |的情况下对三维固定可压缩Navier–Stokes方程进行离散化的收敛结果。与| $ \ gamma> \ frac {3} {2} $ |⁠一起使用。这是具有绝热指数| $ \ gamma $ |的数值方法的第一个收敛结果。少于| $ 3 $ | 当空间维数为3时。考虑的数值方案将对流的有限体积技术与用于扩散的Crouzeix-Raviart有限元相结合。该方案的线性化版本是在法国放射防护学院和法国核医学研究所开发的工业软件CALIF ³ S中实现的。