JOURNAL OF COMPUTATIONAL PHYSICS | 卷:365 |
An exponential time-integrator scheme for steady and unsteady inviscid flows | |
Article | |
Li, Shu-Jie1  Luo, Li-Shi1,2  Wang, Z. J.3  Ju, Lili4  | |
[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China | |
[2] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 23529 USA | |
[3] Univ Kansas, Dept Aerosp Engn, Lawrence, KS 66045 USA | |
[4] Univ South Carolina, Dept Math, Columbia, SC 29208 USA | |
关键词: Exponential time integration; Predictor-corrector method; Large time step; Discontinuous Galerkin; Unstructured meshes; Compressible flow; | |
DOI : 10.1016/j.jcp.2018.03.020 | |
来源: Elsevier | |
【 摘 要 】
An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability and truncation error are analyzed through a one-dimensional model equation. The proposed PCEXP scheme is applied to the Euler equations discretized with a discontinuous Galerkin method in both two and three dimensions. The effectiveness and efficiency of the PCEXP scheme are demonstrated for both steady and unsteady inviscid flows. The accuracy and efficiency of the PCEXP scheme are verified and validated through comparisons with the explicit third-order total variation diminishing Runge-Kutta scheme (TVDRK3), the implicit backward Euler (BE) and the implicit second-order backward difference formula (BDF2). For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time. Moreover, the PCEXP scheme is also shown to achieve the computational efficiency comparable to the implicit schemes for steady flows. (C) 2018 Elsevier Inc. All rights reserved.
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