基于旋转压力校正投影的稳定有限体积法，用于时变不可压缩多流体力学方程

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-10-16 DOI:10.1016/j.cnsns.2024.108389

Xiaoji Song , Xiaochen Chu , Tong Zhang , Pengliang Yang

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引用次数: 0

摘要

本文基于有限体积框架内的旋转压力修正投影法，提出了一种求解时变不可压缩磁流体动力学（MHD）方程的高效数值方案。利用最低等阶混合有限元对（P1-P1-P1）来逼近速度场、磁场和压力场，我们的数值方案通过压力投影稳定来满足离散 inf-sup 条件。为了解决时变不可压缩 MHD 方程中固有的耦合问题，我们引入了旋转压力校正投影法，将原问题分割成多个线性子问题。此外，还给出了数值方案的无条件稳定性，以及数值解的 L2 和 H1 值的最优误差估计。最后，给出了一些数值结果，以验证已建立的理论结论，并显示所考虑的数值方案的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A stabilized finite volume method based on the rotational pressure correction projection for the time-dependent incompressible MHD equations

This paper presents an efficient numerical scheme for solving the time-dependent incompressible Magnetohydrodynamics (MHD) equations based on the rotational pressure correction projection method within the finite volume framework. Utilizing the lowest equal-order mixed finite element pair (

P_{1} - P_{1} - P_{1}

) to approximate the velocity, magnetic and pressure fields, our numerical scheme satisfies the discrete inf–sup condition by the pressure projection stabilization. To tackle the coupling inherent in the time-dependent incompressible MHD equations,the rotational pressure correction projection method is introduced to split the original problem into several linear subproblems. The unconditional stability of numerical schemes are provided,optimal error estimates in both

L^{2}

and

H^{1}

-norms of numerical solutions are also presented. Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical schemes.

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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.