Multilevel Control Variates for Uncertainty Quantification in Simulations of Cloud Cavitation

Abstract

\l\le quant ify uncertainti es in the location and magnitud e of extreme pressure spots revealed from la rge scale multiph ase flow s imul a tions of cloud cavitat ion coll apse. 'vVe examin e clouds containin g 500 cav iti es a nd qu antify uncerta inti es relaLed Lo th eir ini t ial spatial a rrangement. T he resulting 2,000-dimensional s pace is sampl ed using a noninLrusive and com putat ionally effici ent multi level Monte Carlo (JVILMC) methodology. We introduce novel empirically optimal control vari ate coeffici ents to enh ance th e variance reduction in MLMC. The proposed multil evel control vari ates l\tlonLe Carlo leads to more than two orders of magnitude sp eedup when compared Lo st a nd a rd Monte Carlo methods. We id entify large un certa inti es in the locat ion and magnitud e of the peak pressure pu lse a nd present iLs statistical correla tion s and joint proba bility density fun ct ion s wit h the geo metrical characteris tics of the cloud. Characteristic properties of s pati al cloud structure a re identified as potential causes of s ignificant un certa int ies in exe rted collapse pressures. Key words. compressible multiph ase flow , hi gh perform a nce com putin g, diffuse interface met hod, bubble collapse, cloud cav itation , uncerta inty qua ntifica tion , multilevel !\,Jonte Carlo, control va ri ates, fault tolerance

PoUnce: A framework for automatized uncertainty quantification simulations on high-performance clusters

“…Correlations are lower than the ones found in the literature (cf. [27,30]). Possible reasons include the complexity and high sensitivity of the investigated problem, the relatively low grid resolutions, the residual randomness from turbulent fluctuations, and the design and choice of low-fidelity models.…”

“…Debusschere et al, 2017;B. J. Debusschere et al, 2004), UQpy (Olivier et al, 2020), PyMLMC (Sukys et al, 2017), ChaosPy (Feinberg & Langtangen, 2015), UQLab (Marelli & Sudret, 2014), and UQit (Rezaeiravesh et al, 2021). These existing packages often include a large variety of UQ methods, but most do not provide an integrated framework for fully automatized UQ runs.…”