Work

A Second-Order in Time and Energy-Dissipative Scheme for Time-Fractional Navier-Stokes Equations

Year: 2025

Type: article

Abstract: This paper proposes an energy-dissipative scheme for solving two- and three-dimensional time-fractional Navier-Stokes equations. The numerical scheme is constructed, using nonuniform $L2−1σ$ approximation in the temporal direction and the Fourier spectral method in the spatial direction. It is shown that the numerical scheme can keep discrete energy stable and the numerical solutions are uniformly bounded without any restriction on step sizes. Error estimates of the fully-discrete scheme are presented. Moreover, a fast algorithm is applied to accelerate the computation. Numerical results in long time intervals are presented to confirm the effectiveness and high efficiency of the scheme.

Source: Journal of Computational Mathematics

DOI: 10.4208/jcm.2505-m2024-0212

Authors: Ruimin Gao, Dongfang Li, Hongyu Qin

Institutions: Huazhong University of Science and Technology, Wuhan Institute of Technology

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Huazhong University of Science and Technology, Fundamental Research Funds for the Central Universities

Award: G1459676563

OpenAlex ID: W4416685161

FWCI: 0.765

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Cited by: 1

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