An exponential time-integrator scheme for steady and unsteady inviscid flows

Li, Shu-Jie; Luo, Li-Shi; Wang, Z. J.; Ju, Lili

doi:10.1016/j.jcp.2018.03.020

Title: An exponential time-integrator scheme for steady and unsteady inviscid flows

Journal Article · Tue Mar 20 00:00:00 EDT 2018 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2018.03.020· OSTI ID:1538432

Li, Shu-Jie ^[1]; Luo, Li-Shi ^[2];

^[3]; Ju, Lili ^[4]

Beijing Computational Science Research Center, Beijing (China)
Beijing Computational Science Research Center, Beijing (China); Old Dominion University, Norfolk, VA (United States)
University of Kansas, Lawrence, KS (United States)
University of South Carolina, Columbia, SC (United States)

In this report 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.

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Research Organization:: Univ. of South Carolina, Columbia, SC (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); Beijing Computational Science Research Center (CSRC); National Science Foundation (NSF)

Grant/Contract Number:: SC0016540; U1530401; U1501501; DMS-1521965

OSTI ID:: 1538432

Alternate ID(s):: OSTI ID: 1548545

Journal Information:: Journal of Computational Physics, Vol. 365, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 12 works

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