A generalized scalar auxiliary variable approach for the Navier–Stokes-ω/Navier–Stokes-ω equations based on the grad-div stabilization

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-03 DOI:10.1016/j.cnsns.2024.108329

Qinghui Wang, Pengzhan Huang, Yinnian He

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Abstract

In this article, based on the grad-div stabilization, we propose a generalized scalar auxiliary variable approach for solving a fluid–fluid interaction problem governed by the Navier–Stokes- $ω$ /Navier–Stokes- $ω$ equations. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. The proposed scheme is almost unconditionally stable and requires solving only the linear equation with constant coefficient at each time step. It can also penalize for lack of mass conservation and improve the accuracy. Finally, a series of numerical experiments are carried out to illustrate the stability and effectiveness of the proposed scheme.

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基于梯度稳定的纳维-斯托克斯-ω/纳维尔-斯托克斯-ω方程的广义标量辅助变量方法

本文基于梯度离散稳定法，提出了一种广义标量辅助变量方法，用于求解纳维-斯托克斯-ω/纳维尔-斯托克斯-ω方程支配的流体-流体相互作用问题。我们采用了后向欧拉方案和混合有限元近似进行时空离散化，并对界面项和非线性项进行了显式处理。所提出的方案几乎是无条件稳定的，只需在每个时间步求解具有常数系数的线性方程。它还可以对质量不守恒进行惩罚，并提高精度。最后，我们进行了一系列数值实验，以说明所提方案的稳定性和有效性。

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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.