We consider the Navier-Stokes-Fourier system governing the motion of a general compressible, heat conducting, Newtonian fluid driven by random initial/boundary data. Convergence of the stochastic collocation and Monte Carlo numerical methods is shown under the hypothesis that approximate solutions are bounded in probability. Abstract results are illustrated by numerical experiments for the Rayleigh-Benard convection problem.

翻译：我们考虑由随机初/边值驱动的一般可压缩、导热牛顿流体运动的Navier-Stokes-Fourier系统。在近似解依概率有界的假设下，证明了随机配点法和蒙特卡洛数值方法的收敛性。通过瑞利-贝纳德对流传热问题的数值实验对抽象结果进行了验证。