Stochastic turbulence modeling in RANS simulations via multilevel Monte Carlo

Prashant Kumar*, Martin Schmelzer, Richard P. Dwight

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al. (2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level.

Original languageEnglish
Article number104420
Number of pages24
JournalComputers and Fluids
Publication statusPublished - 15 Apr 2020


  • MLMC
  • Random eddy viscosity
  • Random Reynolds stress tensor
  • RANS
  • UQ


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