We prove convergence of a finite difference approximation of the compressible Navier–Stokes system towards the strong solution in \(R^d,\)\(d=2,3,\) for the adiabatic coefficient \(\gamma >1\). Employing the relative energy functional, we find a convergence rate which is uniform in terms of the discretization parameters for \(\gamma > d/2\). All results are unconditional in the sense that we have no assumptions on the regularity nor boundedness of the numerical solution. We also provide numerical experiments to validate the theoretical convergence rate. To the best of our knowledge this work contains the first unconditional result on the convergence of a finite difference scheme for the unsteady compressible Navier–Stokes system in multiple dimensions.

我们证明了绝热系数\（\ gamma> 1 \）的可压缩Navier–Stokes系统向\（R ^ d，\）\（d = 2,3，\）中的强解的有限差分逼近的收敛性。。利用相对能量泛函，我们发现收敛速度在\（\ gamma> d / 2 \）的离散化参数方面是一致的。所有结果均为无条件从某种意义上说，我们对数值解的规律性和有界性没有任何假设。我们还提供了数值实验来验证理论收敛速度。据我们所知，这项工作包含了多维非定常可压缩Navier-Stokes系统有限差分格式收敛的第一个无条件结果。