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

• Published in: Communications in nonlinear science & numerical simulation 2025-01, Vol.140, p.108365, Article 108365
• Main Authors: Jiang, Mengru, Wu, Jilian, Li, Ning, Feng, Xinlong
• Format: Article
• Language: English
• Subjects: Adaptive algorithms; Convergence; Natural convection; Scalar auxiliary variable; Time filter
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.108365

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. •The entire nonlinear term is explicitly processed.•The time precision is improved from the first order to the second order by using the time filter, and the time adaptive structure is constructed.•The proposed method is unconditionally energy stable.