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–Bénard convection problem.

中文翻译：

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不确定初始/边界数据驱动的纳维-斯托克斯-傅立叶系统数值方法的收敛性

我们考虑纳维-斯托克斯-傅里叶系统，它控制由随机初始/边界数据驱动的一般可压缩、导热、牛顿流体的运动。在近似解概率有界的假设下，显示了随机配置和蒙特卡罗数值方法的收敛性。摘要结果通过瑞利-贝纳德对流问题的数值实验进行了说明。