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DOE OSTI · 3007433

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

Breckling, Sean R. [Nevada National Security Site (NNSS), Santa Barbara, CA (United States)] (ORCID:0000000187961119)·Reyes, Jorge [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)] (ORCID:0000000250962297)·Shields, Sidney Ryan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)] (ORCID:0000000317919745)·Watkins, Clifford E. [Nevada National Security Site (NNSS), Santa Barbara, CA (United States)] (ORCID:0000000292884469)
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Abstract

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

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97 MATHEMATICS AND COMPUTINGApproximate deconvolutionBDF2LEFluidsMathematicsScott-VogeulisTime relaxation

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BibTeXRIS

Breckling, Sean R. [Nevada National Security Site (NNSS), Santa Barbara, CA (United States)] (ORCID:0000000187961119), Reyes, Jorge [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)] (ORCID:0000000250962297), Shields, Sidney Ryan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)] (ORCID:0000000317919745), Watkins, Clifford E. [Nevada National Security Site (NNSS), Santa Barbara, CA (United States)] (ORCID:0000000292884469). 2025-12-10. Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation. https://doi.org/10.1016/j.finel.2025.104491

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