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Conservative Model Order Reduction for Fluid Flow

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Quantification of Uncertainty: Improving Efficiency and Technology

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 137 ))

Abstract

In the past decade, model order reduction (MOR) has been successful in reducing the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. Symmetries and conservation laws, which are a distinctive feature of such systems, are often destroyed by conventional MOR techniques which result in a perturbed, and often unstable reduced system. The importance of conservation of energy is well-known for a correct numerical integration of fluid flow. In this paper, we discuss model reduction, that exploits skew-symmetry of conservative and centered discretization schemes, to recover conservation of energy at the level of the reduced system. Moreover, we argue that the reduced system, constructed with the new method, can be identified by a reduced energy that mimics the energy of the high-fidelity system. Therefore, the loss in energy, associated with the model reduction, remains constant in time. This results in an, overall, correct evolution of the fluid that ensures robustness of the reduced system. We evaluate the performance of the proposed method through numerical simulation of various fluid flows, and through a numerical simulation of a continuous variable resonance combustor model.

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Acknowledgements

The work was partially supported by AFOSR under grant FA9550-17-1-9241 and by SNSF under the grant number P1ELP2-175039. We also thank prof. Karen E. Willcox who provided insight and expertise that greatly assisted this work.

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Authors and Affiliations

  1. EPFL, Lausanne, Switzerland

    Babak Maboudi Afkham, Nicolò Ripamonti, Qian Wang & Jan S. Hesthaven

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  1. Babak Maboudi Afkham
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  2. Nicolò Ripamonti
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  3. Qian Wang
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  4. Jan S. Hesthaven
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Correspondence to Babak Maboudi Afkham .

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Editors and Affiliations

  1. Computational Multiscale, Sandia National Laboratories, Albuquerque, NM, USA

    Marta D'Elia

  2. Dept of Scientific Computing, Florida State Univ, Tallahassee, FL, USA

    Max Gunzburger

  3. SISSA mathLab, Mathematics Area, International School for Advanced Studie, Trieste, Italy

    Gianluigi Rozza

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Afkham, B.M., Ripamonti, N., Wang, Q., Hesthaven, J.S. (2020). Conservative Model Order Reduction for Fluid Flow. In: D'Elia, M., Gunzburger, M., Rozza, G. (eds) Quantification of Uncertainty: Improving Efficiency and Technology. Lecture Notes in Computational Science and Engineering, vol 137 . Springer, Cham. https://doi.org/10.1007/978-3-030-48721-8_4

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