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：在本文中，我们将初始数据、外力、粘度系数和导热系数视为可变的数据，用于可压缩Navier-Stokes-Fourier系统。蒙特卡罗方法通常用于逼近统计量，将其与物理空间和时间的适当确定性离散化方法相结合。在假设数值密度和温度在概率上有界的条件下，我们通过应用真正的随机紧性引理证明了随机有限体积解收敛于统计强解。此外，我们展示了蒙特卡罗估计期望和偏差的收敛和误差估计。我们提供了几个数值结果来说明理论结果。