Abstract
The space-time flux reconstruction (FR) approach featuring hyperbolic reformulation of second-order terms is extended to three spatial dimensions and its performance with locallyadaptive pseudo-time stepping schemes is assessed. High-order accurate schemes are generated via the tensor product of the Gauss-Legendre points, for use on 4D hypercube elements. Eigendecomposition of the reformulated equations demonstrates the hyperbolic properties of the new system, in contrast to the parabolic character of the original governing equation. While conventional parabolic schemes can be severely restricted by O(h2) time steps necessary for numerical stability, it is shown that the new approach remains stable for O(h) pseudo-time steps. It was verified that the target order-of-accuracy (OOA) was achieved for schemes involving three spatial dimensions and that O(h) pseudo-time steps were realised. Solving unsteady flow problems in a steady context, with respect to pseudo-time, also allows for the implementation of locally adaptive pseudo-time stepping (LAPTS). This can radically accelerate convergence to the pseudo-steady state for the linear problems investigated compared to traditional time marching procedures, increasing the competitiveness of the new approach for practical CFD analysis.
Original language | English |
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Title of host publication | AIAA AVIATION 2022 Forum: proceedings |
Publisher | American Institute of Aeronautics and Astronautics |
DOIs | |
Publication status | Published - 20 Jun 2022 |
Event | AIAA AVIATION 2022 Forum - Chicago, United States Duration: 27 Jun 2022 → 01 Jul 2022 |
Publication series
Name | AIAA AVIATION 2022 Forum |
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Publisher | American Institute of Aeronautics and Astronautics |
Conference
Conference | AIAA AVIATION 2022 Forum |
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Country/Territory | United States |
City | Chicago |
Period | 27/06/2022 → 01/07/2022 |
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Dive into the research topics of 'A space-time flux reconstruction approach for unsteady 3D parabolic equations with enhanced convergence acceleration'. Together they form a unique fingerprint.Student theses
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Flux reconstruction for high-accuracy aerospace design tools
McCaughtry, T. (Author), Geron, M. (Supervisor), Murphy, A. (Supervisor), Nolan, D. (Supervisor), Watson, R. (Supervisor) & Kim, S. I. (Supervisor), Jul 2024Student thesis: Doctoral Thesis › Doctor of Philosophy
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