Data-Driven Closure of Projection-Based Reduced Order Models for\n Unsteady Compressible Flows Article Swipe
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· 2021
· Open Access
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· DOI: https://doi.org/10.1016/j.cma.2021.114120
· OA: W3198154443
A data-driven closure modeling based on proper orthogonal decomposition (POD)\ntemporal modes is used to obtain stable and accurate reduced order models\n(ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin\nand Petrov-Galerkin projection of the non-conservative compressible\nNavier-Stokes equations. The latter approach is implemented using the\nleast-squares Petrov-Galerkin (LSPG) technique and the present methodology\nallows pre-computation of both Galerkin and LSPG coefficients. Closure is\nperformed by adding linear and non-linear coefficients to the original ROMs and\nminimizing the error with respect to the POD temporal modes. In order to\nfurther reduce the computational cost of the ROMs, an accelerated greedy\nmissing point estimation (MPE) hyper-reduction method is employed. A canonical\ncompressible cylinder flow is first analyzed and serves as a benchmark. The\nsecond problem studied consists of the turbulent flow over a plunging airfoil\nundergoing deep dynamic stall. For the first case, linear and non-linear\nclosure coefficients are both low in intrusiveness, capable of providing\nresults in excellent agreement with the full order model. Regularization of\ncalibrated models is also straightforward for this case. On the other hand, the\ndynamic stall flow is significantly more challenging, specially when only\nlinear coefficients are used. Results show that non-linear calibration\ncoefficients outperform their linear counterparts when a POD basis with fewer\nmodes is used in the reconstruction. However, determining a correct level of\nregularization is more complicated with non-linear coefficients. Hyper-reduced\nmodels show good results when combined with non-linear calibration and an\nappropriate sized POD basis.\n
