In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently used for the approximation of statistical moments, is combined with a suitable deterministic discretisation method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to a statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for the Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.

翻译：本文考虑将可压缩Navier--Stokes--Fourier系统的初始数据、外力、黏性系数及热传导系数设为随机数据。蒙特卡洛方法（常用于统计矩近似）与合理的物理时空确定性离散化方法相结合。在数值密度和温度依概率有界的假设下，我们通过应用严格的随机紧性论证，证明了随机有限体积解收敛到统计强解。进一步，我们给出了期望与偏差的蒙特卡洛估计量的收敛性和误差估计。文中呈现了若干数值结果以阐明理论结论。