Efficient uncertainty quantification of CFD problems by combination of proper orthogonal decomposition and compressed sensing

Arash Mohammadi, Koji Shimoyama, Mohamad Sadeq Karimi, Mehrdad Raisee

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In the current paper, an efficient surrogate model based on combination of Proper Orthogonal Decomposition (POD) and compressed sensing is developed for affordable representation of high dimensional stochastic fields. In the developed method, instead of the full (or classical) Polynomial Chaos Expansion (PCE), the ℓ1-minimization approach is utilized to reduce the computational work-load of the low-fidelity calculations. To assess the model capability in the real engineering problems, two challenging high-dimensional CFD test cases namely; i) turbulent transonic flow around RAE2822 airfoil with 18 geometrical uncertainties and ii) turbulent transonic flow around NASA Rotor 37 with 3 operational and 21 geometrical uncertainties are considered. Results of Uncertainty Quantification (UQ) analysis in both test cases showed that the proposed multi-fidelity approach is able to reproduce the statistics of quantities of interest with much lower computational cost than the classical regression-based PCE method. It is shown that the combination of the POD with the compressed sensing in RAE2822 and Rotor 37 test cases gives respectively computational gains between 1.26–7.72 and 1.79–9.05 times greater than the combination of the POD with the full PCE.

Original languageEnglish
Pages (from-to)187-225
Number of pages39
JournalApplied Mathematical Modelling
Volume94
DOIs
Publication statusPublished - 2021 Jun

Keywords

  • Compressed sensing
  • Multifidelity
  • Polynomial chaos expansion
  • Proper orthogonal decomposition
  • Uncertainty quantification

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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