Stability, convergence, and energy preservation robust methods for fully implicit and fully explicit coupling schemes

IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2025-05-01 Epub Date: 2025-03-01 DOI:10.1016/j.chaos.2025.116131
Taj Munir , Can Kang , Hongchu Chen , Hussan Zeb , Muhammad Naveed Khan , Muhammad Usman Farid
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Abstract

This paper presents an analysis of the Godunov–Ryabenkii stability, Generalized Mini-mal Residual(GMRES) convergence, and energy-preserving properties of partitioned and monolithic approaches (fully implicit and fully explicit schemes) for solving coupled parabolic problems. Specifically, we consider a bi-domain parabolic diffusion problem with two types of coupling conditions at the interface: Dirichlet–Neumann and heat-flux coupling. Our findings shows that the Dirichlet–Neumann coupling is unconditionally stable for both approaches. In contrast, the heat-flux coupling requires additional conditions to ensure the stability of the coupled problem. For numerical approximations, finite volume and finite difference schemes are used. The results show that energy preservation is achieved with one-sided differences in the finite volume method, while the finite difference method achieves conservation when central difference approximations are used for both the coupling and boundary conditions in the heat-flux coupling case. Additionally, Dirichlet–Neumann coupling maintains stability and energy preservation in both methods using the one-sided approach without requiring extra conditions. However, for heat-flux coupling, an additional restriction is necessary to ensure stability. The challenge for the convergence of coupled interface problems arise due to strong domain interactions and sensitive interface conditions, like Dirichlet–Neumann or heat-flux coupling. The poor system conditioning and discretization choices can slow the rate of convergence. For this purpose we used the GMRES method. This work provides a comprehensive framework for addressing coupled parabolic diffusion problems using robust, stable, and energy-preserving numerical methods.
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全隐式和全显式耦合方案的稳定性、收敛性和节能鲁棒方法
本文分析了求解耦合抛物问题的分段和整体方法(全隐式和全显式格式)的Godunov-Ryabenkii稳定性、广义极小残差(GMRES)收敛性和保能性。具体来说,我们考虑了一个双域抛物扩散问题,该问题在界面处具有两种耦合条件:Dirichlet-Neumann和热通量耦合。我们的发现表明Dirichlet-Neumann耦合对两种方法都是无条件稳定的。相反,热流耦合需要附加条件来保证耦合问题的稳定性。对于数值近似,采用有限体积格式和有限差分格式。结果表明,有限体积法在单侧差分条件下实现了能量守恒,而在热流耦合情况下,对耦合和边界条件均采用中心差分近似时,有限差分法实现了能量守恒。此外,Dirichlet-Neumann耦合在不需要额外条件的情况下使用单侧方法保持了两种方法的稳定性和能量保存。然而,对于热流耦合,需要一个额外的限制来确保稳定性。耦合界面问题收敛的挑战是由于强域相互作用和敏感的界面条件,如狄利克雷-诺伊曼或热通量耦合。不良的系统调节和离散化选择会减慢收敛速度。为此,我们使用了GMRES方法。这项工作为解决耦合抛物扩散问题提供了一个全面的框架,使用鲁棒,稳定和能量守恒的数值方法。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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