We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and deterministic errors are analyzed up to a stopping time of the exact solution. On the life-span of an exact strong solution we prove the convergence of the numerical solutions. Numerical experiments illustrate rich dynamics of random viscous compressible magnetohydrodynamics.

翻译：本文研究随机可压缩黏性磁流体动力学流动。通过将蒙特卡洛方法与确定性有限体积法相结合，我们对随机系统进行数值求解。在精确解的停时范围内，分析了包含统计误差与确定性误差的定量误差估计。在精确强解的存在时间内，我们证明了数值解的收敛性。数值实验展示了随机黏性可压缩磁流体动力学丰富的动力学行为。