A decoupled, linearly implicit and high-order structure-preserving scheme for Euler–Poincaré equations

Ruimin Gao, Dongfang Li, Ming Mei and Dan Zhao

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 218, issue C, 679-703

Abstract: It is challenging to develop high-order structure-preserving finite difference schemes for the modified two-component Euler–Poincaré equations due to the nonlinear terms and high-order derivative terms. To overcome the difficulties, we introduce a bi-variate function and carefully choose the intermediate average variable in the temporal discretization. Then, we obtain a decoupled and linearly implicit scheme. It is shown that the fully-discrete scheme can keep both the discrete mass and energy conserved. And the fully-discrete scheme has fourth-order accuracy in the spatial direction and second-order accuracy in the temporal direction. Several numerical examples are given to confirm the theoretical results.

Keywords: Decoupled scheme; High-order accuracy; Modified two-component Euler–Poincaré equations; Mass conservation; Energy stability (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:218:y:2024:i:c:p:679-703

DOI: 10.1016/j.matcom.2023.12.009

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