A fully discrete finite element method for unsteady magnetohydrodynamic flow in porous media

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-04 DOI:10.1016/j.cnsns.2025.108735

Qianqian Ding , Shipeng Mao , Xiaorong Wang

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引用次数: 0

Abstract

This article explores the unsteady magnetohydrodynamic (MHD) model within the framework of porous media flow. This model consists of the Brinkman–Forchheimer equations and Maxwell equations in the porous media domain, which are coupled by the Lorentz force. We propose and analyze a numerical discretization method for MHD porous model. The second-order backward difference formula is utilized for temporal derivative terms, and the mixed finite element method is employed for spatial discretization. Rigorous proofs of stability and uniqueness are provided for the numerical solutions. We establish optimal

L^{2}

-error estimates for the velocity and magnetic induction without imposing constraints on the relationship between the time step and mesh size. Finally, several three-dimensional numerical experiments are performed to illustrate the features of the proposed numerical method and validate the theoretical findings. To our knowledge, this is the first error analysis and simulation to address unsteady MHD flow through porous media.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.