An analysis of second-order sav-filtered time-stepping finite element method for unsteady natural convection problems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-25 DOI:10.1016/j.cnsns.2024.108365

Mengru Jiang , Jilian Wu , Ning Li , Xinlong Feng

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Abstract

This paper presents an unconditionally stable time-filtering algorithm for natural convection equations. The algorithm is based on the scalar auxiliary variables in the exponential function and adopts a completely discrete Back-Euler combining time filter scheme. The proposed scheme requires minimal invasive modification of the existing program to improve the time accuracy from first-order to second-order without increasing the computational complexity, and we demonstrate the unconditional stability of the proposed algorithm and analyze its second-order convergence. In addition, due to the increasing demand for low-memory solvers, the application of a time-adaptive algorithm can improve the accuracy and efficiency of the proposed algorithm, so we extend the method to variable step sizes and construct an adaptive algorithm. Finally, the effectiveness of the proposed method and the accuracy of the theoretical results are verified by numerical experiments.

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针对非稳态自然对流问题的二阶 sav 滤波时间步进有限元法分析

本文提出了一种无条件稳定的自然对流方程时间滤波算法。该算法基于指数函数中的标量辅助变量，采用完全离散的 Back-Euler 结合时间滤波方案。提出的方案只需对现有程序进行微创修改，就能在不增加计算复杂度的情况下将时间精度从一阶提高到二阶，我们证明了所提算法的无条件稳定性，并分析了其二阶收敛性。此外，由于对低内存求解器的要求越来越高，应用时间自适应算法可以提高所提算法的精度和效率，因此我们将该方法扩展到可变步长，并构建了自适应算法。最后，我们通过数值实验验证了所提方法的有效性和理论结果的准确性。

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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.