A nonintrusive reduced order model for nonlinear transient thermal problems with nonparametrized variability

In this work, we consider a transient thermal problem, with a nonlinear term coming from the radiation boundary condition and a nonparametrized variability in the form complex scenarios for the initial condition and the convection coefficients and external temperatures. We use a posteriori reduced o...

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Bibliographic Details
Published in:	Advanced modeling and simulation in engineering sciences Vol. 7; no. 1; pp. 1 - 19
Main Authors:	Casenave, Fabien, Gariah, Asven, Rey, Christian, Feyel, Frederic
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 07-05-2020 Springer Nature B.V Springer SpringerOpen
Series:	State-of-the-Art Model Order Reduction and Its Applications in 2020
Subjects:	Accuracy Aircraft engines Boundary conditions Classical and Continuum Physics Compressors Computational Science and Engineering Empirical cubature method Engineering Engineering Sciences Nonlinear transient heat equation Nonlinearity Nonparametrized variability Polynomials Proper Orthogonal Decomposition Radiation boundary condition Reduced order modeling Reduced order models Research Article Software State-of-the-Art Model Order Reduction and Its Applications in 2020 Theoretical and Applied Mechanics Tolerances Nonlinear transient heat equation Proper orthogonal decomposition Nonparametrized variability Radiation boundary condition Empirical cubature method Reduced order modeling
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Summary:	In this work, we consider a transient thermal problem, with a nonlinear term coming from the radiation boundary condition and a nonparametrized variability in the form complex scenarios for the initial condition and the convection coefficients and external temperatures. We use a posteriori reduced order modeling by snapshot Proper Orthogonal Decomposition. To treat the nonlinearity, hyperreduction is required in our case, since precomputing the polynomial nonlinearities becomes too expensive for the radiation term. We applied the Empirical Cubature Method, originally proposed for nonlinear structural mechanics, to our particular problem. We apply the method to the design of high-pressure compressors for civilian aircraft engines, where a fast evaluation of the solution temperature is required when testing new configurations. We also illustrate that when using in the reduced solver the same model as the one from the high-fidelity code, the approximation is very accurate. However, when using a commercial code to generate the high-fidelity data, where the implementation of the model and solver is unknown, the reduced model is less accurate but still within engineering tolerances in our tests. Hence, the regularizing property of reduced order models, together with a nonintrusive approach, enables the use of commercial software to generate the data, even under some degree of uncertainty in the proprietary model or solver of the commercial software.
ISSN:	2213-7467 2213-7467
DOI:	10.1186/s40323-020-00156-3