Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows

Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows

Year:    2022

Author:    Jian Yu, Deep Ray, Jan S. Hesthaven

Communications in Computational Physics, Vol. 32 (2022), Iss. 3 : pp. 595–637

Abstract

A projection-based reduced order model (ROM) based on the Fourier collocation method is proposed for compressible flows. The incorporation of localized artificial viscosity model and filtering is pursued to enhance the robustness and accuracy of the ROM for shock-dominated flows. Furthermore, for Euler systems, ROMs built on the conservative and the skew-symmetric forms of the governing equation are compared. To ensure efficiency, the discrete empirical interpolation method (DEIM) is employed. An alternative reduction approach, exploring the sparsity of viscosity is also investigated for the viscous terms. A number of one- and two-dimensional benchmark cases are considered to test the performance of the proposed models. Results show that stable computations for shock-dominated cases can be achieved with ROMs built on both the conservative and the skew-symmetric forms without additional stabilization components other than the viscosity model and filtering. Under the same parameters, the skew-symmetric form shows better robustness and accuracy than its conservative counterpart, while the conservative form is superior in terms of efficiency.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2021-0180

Communications in Computational Physics, Vol. 32 (2022), Iss. 3 : pp. 595–637

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    43

Keywords:    Projection-based reduced order modeling Fourier collocation artificial viscosity compressible flow.

Author Details

Jian Yu

Deep Ray

Jan S. Hesthaven